diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index b4897c9..b5b6b65 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -240,6 +240,31 @@
             self.assertTrue(s == s, "{%r} not equal to itself" % f)
             self.assertTrue(d == d, "{%r : None} not equal to itself" % f)
 
+    def assertEqualAndEqualSign(self, a, b):
+        # fail unless a == b and a and b have the same sign bit;
+        # the only difference from assertEqual is that this test
+        # distingishes -0.0 and 0.0.
+        self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
+
+    @requires_IEEE_754
+    def test_float_mod(self):
+        # Check behaviour of % operator for IEEE 754 special cases.
+        # In particular, check signs of zeros.
+        mod = operator.mod
+
+        self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0)
+        self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0)
+        self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0)
+        self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0)
+        self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100)
+        self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0)
+
+        self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0)
+        self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100)
+        self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0)
+        self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0)
+        self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0)
+        self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0)
 
 
 class FormatFunctionsTestCase(unittest.TestCase):
diff --git a/Misc/NEWS b/Misc/NEWS
index 1c7abf7..76ccf7a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,10 @@
 Core and Builtins
 -----------------
 
+- Issue #10596: Fix float.__mod__ to have the same behaviour as
+  float.__divmod__ with respect to signed zeros.  -4.0 % 4.0 should be
+  0.0, not -0.0.
+
 Library
 -------
 
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 865c960..6a2af74 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -600,10 +600,20 @@
 #endif
     PyFPE_START_PROTECT("modulo", return 0)
     mod = fmod(vx, wx);
-    /* note: checking mod*wx < 0 is incorrect -- underflows to
-       0 if wx < sqrt(smallest nonzero double) */
-    if (mod && ((wx < 0) != (mod < 0))) {
-        mod += wx;
+    if (mod) {
+        /* ensure the remainder has the same sign as the denominator */
+        if ((wx < 0) != (mod < 0)) {
+            mod += wx;
+        }
+    }
+    else {
+        /* the remainder is zero, and in the presence of signed zeroes
+           fmod returns different results across platforms; ensure
+           it has the same sign as the denominator; we'd like to do
+           "mod = wx * 0.0", but that may get optimized away */
+        mod *= mod;  /* hide "mod = +0" from optimizer */
+        if (wx < 0.0)
+            mod = -mod;
     }
     PyFPE_END_PROTECT(mod)
     return PyFloat_FromDouble(mod);