diff --git a/SRC/chgeqz.f b/SRC/chgeqz.f
index bcf5acd0bf..a158ee8398 100644
--- a/SRC/chgeqz.f
+++ b/SRC/chgeqz.f
@@ -518,13 +518,17 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
          IF( ILAST.EQ.ILO ) THEN
             GO TO 60
          ELSE
-            IF( ABS1( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+            IF( ABS1( H( ILAST, ILAST-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS1( H( ILAST, ILAST ) ) + ABS1( H( ILAST-1, ILAST-1 ) 
+     $         ) ) ) ) THEN
                H( ILAST, ILAST-1 ) = CZERO
                GO TO 60
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
+     $          ) ) ) ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -538,7 +542,9 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS1( H( J, J-1 ) ).LE.ATOL ) THEN
+               IF( ABS1( H( J, J-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $            ABS1( H( J, J ) ) + ABS1( H( J-1, J-1 ) ) 
+     $            ) ) ) THEN
                   H( J, J-1 ) = CZERO
                   ILAZRO = .TRUE.
                ELSE
@@ -548,7 +554,10 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+            TEMP = ABS ( T( J, J + 1 ) )
+            IF ( J .GT. ILO )
+     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
+            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/dhgeqz.f b/SRC/dhgeqz.f
index 99557f20eb..655351386a 100644
--- a/SRC/dhgeqz.f
+++ b/SRC/dhgeqz.f
@@ -531,13 +531,17 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
             GO TO 80
          ELSE
-            IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+            IF( ABS( H( ILAST, ILAST-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( H( ILAST, ILAST ) ) + ABS( H( ILAST-1, ILAST-1 ) ) 
+     $         ) ) ) THEN
                H( ILAST, ILAST-1 ) = ZERO
                GO TO 80
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
+     $          ) ) ) ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -551,7 +555,9 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
+               IF( ABS( H( J, J-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( H( J, J ) ) + ABS( H( J-1, J-1 ) ) 
+     $         ) ) ) THEN
                   H( J, J-1 ) = ZERO
                   ILAZRO = .TRUE.
                ELSE
@@ -561,7 +567,10 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+            TEMP = ABS ( T( J, J + 1 ) )
+            IF ( J .GT. ILO )
+     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
+            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/shgeqz.f b/SRC/shgeqz.f
index 34f6a8ce0d..cfed49e5aa 100644
--- a/SRC/shgeqz.f
+++ b/SRC/shgeqz.f
@@ -531,13 +531,17 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
             GO TO 80
          ELSE
-            IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+            IF( ABS( H( ILAST, ILAST-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( H( ILAST, ILAST ) ) + ABS( H( ILAST-1, ILAST-1 ) ) 
+     $         ) ) ) THEN
                H( ILAST, ILAST-1 ) = ZERO
                GO TO 80
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
+     $          ) ) ) ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -551,7 +555,9 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
+               IF( ABS( H( J, J-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( H( J, J ) ) + ABS( H( J-1, J-1 ) ) 
+     $         ) ) ) THEN
                   H( J, J-1 ) = ZERO
                   ILAZRO = .TRUE.
                ELSE
@@ -561,7 +567,10 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+            TEMP = ABS ( T( J, J + 1 ) )
+            IF ( J .GT. ILO )
+     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
+            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/zhgeqz.f b/SRC/zhgeqz.f
index 9602447272..4b9c7a7611 100644
--- a/SRC/zhgeqz.f
+++ b/SRC/zhgeqz.f
@@ -519,13 +519,17 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
          IF( ILAST.EQ.ILO ) THEN
             GO TO 60
          ELSE
-            IF( ABS1( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+            IF( ABS1( H( ILAST, ILAST-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS1( H( ILAST, ILAST ) ) + ABS1( H( ILAST-1, ILAST-1 ) 
+     $         ) ) ) ) THEN
                H( ILAST, ILAST-1 ) = CZERO
                GO TO 60
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
+     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
+     $          ) ) ) ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -539,7 +543,9 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS1( H( J, J-1 ) ).LE.ATOL ) THEN
+               IF( ABS1( H( J, J-1 ) ).LE.MAX( SAFMIN, ULP*( 
+     $            ABS1( H( J, J ) ) + ABS1( H( J-1, J-1 ) ) 
+     $            ) ) ) THEN
                   H( J, J-1 ) = CZERO
                   ILAZRO = .TRUE.
                ELSE
@@ -549,7 +555,10 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+            TEMP = ABS ( T( J, J + 1 ) )
+            IF ( J .GT. ILO )
+     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
+            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A