diff --git a/rest_framework/schemas/openapi.py b/rest_framework/schemas/openapi.py
index 58788bc234..1df132ce32 100644
--- a/rest_framework/schemas/openapi.py
+++ b/rest_framework/schemas/openapi.py
@@ -32,39 +32,30 @@ def get_info(self):
 
         return info
 
-    def get_paths(self, request=None):
-        result = {}
-
-        paths, view_endpoints = self._get_paths_and_endpoints(request)
-
-        # Only generate the path prefix for paths that will be included
-        if not paths:
-            return None
+    def get_schema(self, request=None, public=False):
+        """
+        Generate a OpenAPI schema.
+        """
+        self._initialise_endpoints()
 
+        # Iterate endpoints generating per method path operations.
+        # TODO: …and reference components.
+        paths = {}
+        _, view_endpoints = self._get_paths_and_endpoints(None if public else request)
         for path, method, view in view_endpoints:
             if not self.has_view_permissions(path, method, view):
                 continue
+
             operation = view.schema.get_operation(path, method)
             # Normalise path for any provided mount url.
             if path.startswith('/'):
                 path = path[1:]
             path = urljoin(self.url or '/', path)
 
-            result.setdefault(path, {})
-            result[path][method.lower()] = operation
-
-        return result
-
-    def get_schema(self, request=None, public=False):
-        """
-        Generate a OpenAPI schema.
-        """
-        self._initialise_endpoints()
-
-        paths = self.get_paths(None if public else request)
-        if not paths:
-            return None
+            paths.setdefault(path, {})
+            paths[path][method.lower()] = operation
 
+        # Compile final schema.
         schema = {
             'openapi': '3.0.2',
             'info': self.get_info(),
diff --git a/tests/schemas/test_openapi.py b/tests/schemas/test_openapi.py
index 03eb9de7a9..8a723b85d9 100644
--- a/tests/schemas/test_openapi.py
+++ b/tests/schemas/test_openapi.py
@@ -659,7 +659,7 @@ def test_paths_construction(self):
         generator = SchemaGenerator(patterns=patterns)
         generator._initialise_endpoints()
 
-        paths = generator.get_paths()
+        paths = generator.get_schema()["paths"]
 
         assert '/example/' in paths
         example_operations = paths['/example/']
@@ -676,7 +676,7 @@ def test_prefixed_paths_construction(self):
         generator = SchemaGenerator(patterns=patterns)
         generator._initialise_endpoints()
 
-        paths = generator.get_paths()
+        paths = generator.get_schema()["paths"]
 
         assert '/v1/example/' in paths
         assert '/v1/example/{id}/' in paths
@@ -689,7 +689,7 @@ def test_mount_url_prefixed_to_paths(self):
         generator = SchemaGenerator(patterns=patterns, url='/api')
         generator._initialise_endpoints()
 
-        paths = generator.get_paths()
+        paths = generator.get_schema()["paths"]
 
         assert '/api/example/' in paths
         assert '/api/example/{id}/' in paths
@@ -707,6 +707,15 @@ def test_schema_construction(self):
         assert 'openapi' in schema
         assert 'paths' in schema
 
+    def test_schema_with_no_paths(self):
+        patterns = []
+        generator = SchemaGenerator(patterns=patterns)
+
+        request = create_request('/')
+        schema = generator.get_schema(request=request)
+
+        assert schema['paths'] == {}
+
     def test_schema_information(self):
         """Construction of the top level dictionary."""
         patterns = [