diff --git a/Lib/multiprocessing/pool.py b/Lib/multiprocessing/pool.py
index 99b4df4..170aa7f 100644
--- a/Lib/multiprocessing/pool.py
+++ b/Lib/multiprocessing/pool.py
@@ -576,6 +576,7 @@
         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 0fe6497..42b2d91 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1152,6 +1152,18 @@
         join()
         self.assertTrue(join.elapsed < 0.2)
 
+    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 unpickleable_result():
     return lambda: 42
 
@@ -2113,7 +2125,7 @@
         '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')
@@ -2127,7 +2139,7 @@
     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')
@@ -2141,7 +2153,7 @@
         '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 d8d5199..b832384 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -67,6 +67,9 @@
 Library
 -------
 
+- Issue #12157: Make pool.map() empty iterables correctly.  Initial
+  patch by mouad.
+
 - Issue #14962: Update text coloring in IDLE shell window after changing
   options.  Patch by Roger Serwy.