diff --git a/CHANGES.md b/CHANGES.md
index 1eb1229261ad..ec998f6c1c16 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -63,6 +63,7 @@
 
 ## Bugfixes
 
+* (Python/YAML) Fixed SQL-backed `Combine` generating an invalid `GROUP BY ` clause for global aggregations when `group_by` is empty or omitted ([#41047](https://github.com/apache/beam/issues/41047)).
 * (Java) Improved the error message when decoding with a ProtoCoder for the raw `com.google.protobuf.Message` type (for example inferred from a generic `T extends Message`): it now explains how to fix it instead of surfacing a `NoSuchMethodException` ([#19713](https://github.com/apache/beam/issues/19713)).
 * Fixed X (Java/Python) ([#X](https://github.com/apache/beam/issues/X)).
 
diff --git a/sdks/python/apache_beam/yaml/yaml_combine.py b/sdks/python/apache_beam/yaml/yaml_combine.py
index d32b5272106e..e5452f3ec9f9 100644
--- a/sdks/python/apache_beam/yaml/yaml_combine.py
+++ b/sdks/python/apache_beam/yaml/yaml_combine.py
@@ -64,7 +64,9 @@ def normalize_combine(spec):
   from apache_beam.yaml.yaml_transform import SafeLineLoader
   if spec['type'] == 'Combine':
     config = spec.get('config')
-    if isinstance(config.get('group_by'), str):
+    if not config.get('group_by'):
+      config['group_by'] = []
+    elif isinstance(config['group_by'], str):
       config['group_by'] = [config['group_by']]
 
     def normalize_agg(dest, agg):
@@ -103,11 +105,11 @@ class PyJsYamlCombine(beam.PTransform):
   """
   def __init__(
       self,
-      group_by: Iterable[str],
-      combine: Mapping[str, Mapping[str, Any]],
+      group_by: Iterable[str] = (),
+      combine: Optional[Mapping[str, Mapping[str, Any]]] = None,
       language: Optional[str] = None):
-    self._group_by = group_by
-    self._combine = combine
+    self._group_by = tuple(group_by or ())
+    self._combine = combine or {}
     self._language = language
 
   def expand(self, pcoll):
@@ -180,7 +182,12 @@ def extract_return_type(expr):
 
 @beam.ptransform.ptransform_fn
 def _SqlCombineTransform(
-    pcoll, sql_transform_constructor, group_by, combine, language=None):
+    pcoll,
+    sql_transform_constructor,
+    group_by: Iterable[str] = (),
+    combine: Optional[Mapping[str, Any]] = None,
+    language: Optional[str] = None):
+  group_by = list(group_by or [])
   all_fields = [
       x for x, _ in named_fields_from_element_type(pcoll.element_type)
   ]
@@ -198,14 +205,18 @@ def combine_col(dest, fn_spec):
       expr = fn_spec['fn']['type']
     return f'{expr} as {dest}'
 
-  return pcoll | sql_transform_constructor(
-      'SELECT %s FROM PCOLLECTION GROUP BY %s' % (
-          ', '.join(
-              list(group_by) +
-              [combine_col(dest, fn_spec)
-               for dest, fn_spec in combine.items()]),
-          ', '.join(group_by),
-      ))
+  select_cols = group_by + [
+      combine_col(dest, fn_spec) for dest, fn_spec in (combine or {}).items()
+  ]
+  if group_by:
+    query = 'SELECT %s FROM PCOLLECTION GROUP BY %s' % (
+        ', '.join(select_cols),
+        ', '.join(group_by),
+    )
+  else:
+    query = 'SELECT %s FROM PCOLLECTION' % ', '.join(select_cols)
+
+  return pcoll | sql_transform_constructor(query)
 
 
 def create_combine_providers():
diff --git a/sdks/python/apache_beam/yaml/yaml_combine_test.py b/sdks/python/apache_beam/yaml/yaml_combine_test.py
index caf3de10078b..a9deff6c9a95 100644
--- a/sdks/python/apache_beam/yaml/yaml_combine_test.py
+++ b/sdks/python/apache_beam/yaml/yaml_combine_test.py
@@ -21,6 +21,7 @@
 import apache_beam as beam
 from apache_beam.testing.util import assert_that
 from apache_beam.testing.util import equal_to
+from apache_beam.yaml.yaml_combine import _SqlCombineTransform
 from apache_beam.yaml.yaml_transform import YamlTransform
 
 DATA = [
@@ -90,6 +91,61 @@ def test_no_keys(self):
               beam.Row(c=410),
           ]))
 
+  def test_no_keys_omitted(self):
+    with beam.Pipeline(options=beam.options.pipeline_options.PipelineOptions(
+        pickle_library='cloudpickle')) as p:
+      elements = p | beam.Create(DATA)
+      result = elements | YamlTransform(
+          '''
+          type: Combine
+          config:
+            combine:
+              c: sum
+          ''')
+      assert_that(
+          result | beam.Map(lambda x: beam.Row(**x._asdict())),
+          equal_to([
+              beam.Row(c=410),
+          ]))
+
+  def test_sql_combine_query_generation(self):
+    queries = []
+    pcoll = beam.Pipeline() | beam.Create(DATA)
+
+    # With grouping keys: GROUP BY clause must be generated.
+    _ = pcoll | _SqlCombineTransform(
+        lambda q: queries.append(q) or beam.Map(lambda x: x),
+        group_by=['a'],
+        combine={'total_c': {
+            'fn': {
+                'type': 'sum'
+            }, 'value': 'c'
+        }})
+    self.assertEqual(
+        queries[-1], 'SELECT a, sum(c) as total_c FROM PCOLLECTION GROUP BY a')
+
+    # Without grouping keys (group_by=[]): GROUP BY clause must be omitted.
+    _ = pcoll | _SqlCombineTransform(
+        lambda q: queries.append(q) or beam.Map(lambda x: x),
+        group_by=[],
+        combine={'total_c': {
+            'fn': {
+                'type': 'sum'
+            }, 'value': 'c'
+        }})
+    self.assertEqual(queries[-1], 'SELECT sum(c) as total_c FROM PCOLLECTION')
+
+    # With omitted grouping keys (group_by=None): GROUP BY clause must be omitted.
+    _ = pcoll | _SqlCombineTransform(
+        lambda q: queries.append(q) or beam.Map(lambda x: x),
+        group_by=None,
+        combine={'total_c': {
+            'fn': {
+                'type': 'sum'
+            }, 'value': 'c'
+        }})
+    self.assertEqual(queries[-1], 'SELECT sum(c) as total_c FROM PCOLLECTION')
+
   def test_multiple_combines(self):
     with beam.Pipeline(options=beam.options.pipeline_options.PipelineOptions(
         pickle_library='cloudpickle')) as p: