diff --git a/Lib/test/test_datetime.py b/Lib/test/test_datetime.py
index 436cfcad750..f2f3a87478f 100644
--- a/Lib/test/test_datetime.py
+++ b/Lib/test/test_datetime.py
@@ -1425,6 +1425,15 @@ class TestDateTime(TestDate):
             self.assertRaises(ValueError, self.theclass.utcfromtimestamp,
                               insane)
 
+    def test_negative_float_fromtimestamp(self):
+        # The result is tz-dependent; at least test that this doesn't
+        # fail (like it did before bug 1646728 was fixed).
+        self.theclass.fromtimestamp(-1.05)
+
+    def test_negative_float_utcfromtimestamp(self):
+        d = self.theclass.utcfromtimestamp(-1.05)
+        self.assertEquals(d, self.theclass(1969, 12, 31, 23, 59, 58, 950000))
+
     def test_utcnow(self):
         import time
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 3cefca9fcf0..c51b690d42c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -118,6 +118,9 @@ Core and builtins
 Extension Modules
 -----------------
 
+- Patch #1646728: datetime.fromtimestamp fails with negative
+  fractional times.  With unittest.
+
 - Patch #1494140: Add documentation for the new struct.Struct object.
 
 - Patch #1657276: Make NETLINK_DNRTMSG conditional.
diff --git a/Modules/datetimemodule.c b/Modules/datetimemodule.c
index 9ae77326b66..8207ffd0c9b 100644
--- a/Modules/datetimemodule.c
+++ b/Modules/datetimemodule.c
@@ -3686,6 +3686,12 @@ datetime_from_timestamp(PyObject *cls, TM_FUNC f, double timestamp,
 		return NULL;
 	fraction = timestamp - (double)timet;
 	us = (int)round_to_long(fraction * 1e6);
+	if (us < 0) {
+		/* Truncation towards zero is not what we wanted
+		   for negative numbers (Python's mod semantics) */
+		timet -= 1;
+		us += 1000000;
+	}
 	/* If timestamp is less than one microsecond smaller than a
 	 * full second, round up. Otherwise, ValueErrors are raised
 	 * for some floats. */