diff --git a/jupyter_client/tests/test_jsonutil.py b/jupyter_client/tests/test_jsonutil.py
index 9583a22c8..13ade51ec 100644
--- a/jupyter_client/tests/test_jsonutil.py
+++ b/jupyter_client/tests/test_jsonutil.py
@@ -45,11 +45,11 @@ def test_parse_ms_precision():
     base = '2013-07-03T16:34:52'
     digits = '1234567890'
     
-    parsed = jsonutil.parse_date(base)
+    parsed = jsonutil.parse_date(base+'Z')
     assert isinstance(parsed, datetime.datetime)
     for i in range(len(digits)):
         ts = base + '.' + digits[:i]
-        parsed = jsonutil.parse_date(ts)
+        parsed = jsonutil.parse_date(ts+'Z')
         if i >= 1 and i <= 6:
             assert isinstance(parsed, datetime.datetime)
         else: