diff --git a/Lib/multiprocessing/pool.py b/Lib/multiprocessing/pool.py
index 0c29e644ffd..ccee9612d4c 100644
--- a/Lib/multiprocessing/pool.py
+++ b/Lib/multiprocessing/pool.py
@@ -584,6 +584,7 @@ class MapResult(ApplyResult):
         if chunksize <= 0:
             self._number_left = 0
             self._ready = True
+            del cache[self._job]
         else:
             self._number_left = length//chunksize + bool(length % chunksize)
 
diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index 5f1bba32a27..0d98a1498c7 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1178,6 +1178,18 @@ class _TestPool(BaseTestCase):
         join()
         self.assertLess(join.elapsed, 0.5)
 
+    def test_empty_iterable(self):
+        # See Issue 12157
+        p = self.Pool(1)
+
+        self.assertEqual(p.map(sqr, []), [])
+        self.assertEqual(list(p.imap(sqr, [])), [])
+        self.assertEqual(list(p.imap_unordered(sqr, [])), [])
+        self.assertEqual(p.map_async(sqr, []).get(), [])
+
+        p.close()
+        p.join()
+
 def raising():
     raise KeyError("key")
 
@@ -2176,7 +2188,7 @@ class ProcessesMixin(object):
         'Queue', 'Lock', 'RLock', 'Semaphore', 'BoundedSemaphore',
         'Condition', 'Event', 'Value', 'Array', 'RawValue',
         'RawArray', 'current_process', 'active_children', 'Pipe',
-        'connection', 'JoinableQueue'
+        'connection', 'JoinableQueue', 'Pool'
         )))
 
 testcases_processes = create_test_cases(ProcessesMixin, type='processes')
@@ -2190,7 +2202,7 @@ class ManagerMixin(object):
     locals().update(get_attributes(manager, (
         'Queue', 'Lock', 'RLock', 'Semaphore', 'BoundedSemaphore',
        'Condition', 'Event', 'Value', 'Array', 'list', 'dict',
-        'Namespace', 'JoinableQueue'
+        'Namespace', 'JoinableQueue', 'Pool'
         )))
 
 testcases_manager = create_test_cases(ManagerMixin, type='manager')
@@ -2204,7 +2216,7 @@ class ThreadsMixin(object):
         'Queue', 'Lock', 'RLock', 'Semaphore', 'BoundedSemaphore',
         'Condition', 'Event', 'Value', 'Array', 'current_process',
         'active_children', 'Pipe', 'connection', 'dict', 'list',
-        'Namespace', 'JoinableQueue'
+        'Namespace', 'JoinableQueue', 'Pool'
         )))
 
 testcases_threads = create_test_cases(ThreadsMixin, type='threads')
diff --git a/Misc/NEWS b/Misc/NEWS
index 2890ebee4f7..071e962690c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -70,6 +70,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #12157: Make pool.map() empty iterables correctly.  Initial
+  patch by mouad.
+
 - Issue #14992: os.makedirs(path, exist_ok=True) would raise an OSError
   when the path existed and had the S_ISGID mode bit set when it was
   not explicitly asked for.  This is no longer an exception as mkdir