diff --git a/Lib/fontMath/mathKerning.py b/Lib/fontMath/mathKerning.py
index dd25bbb..47958cf 100644
--- a/Lib/fontMath/mathKerning.py
+++ b/Lib/fontMath/mathKerning.py
@@ -19,13 +19,14 @@ class kerning dictionary.
 
 class MathKerning(object):
 
-    def __init__(self, kerning=None, groups=None):
+    def __init__(self, kerning=None, groups=None, strictGroups=False):
         if kerning is None:
             kerning = {}
         if groups is None:
             groups = {}
         self.update(kerning)
         self.updateGroups(groups)
+        self.strictGroups = strictGroups
 
     # -------
     # Loading
@@ -168,6 +169,11 @@ def __sub__(self, other):
         return k
 
     def _processMathOne(self, other, funct):
+        g1 = self.groups()
+        g2 = other.groups()
+        if self.strictGroups or other.strictGroups:
+            if g1 != g2:
+                raise ValueError("Kerning groups must be exactly the same.")
         comboPairs = set(self._kerning.keys()) | set(other._kerning.keys())
         kerning = dict.fromkeys(comboPairs, None)
         for k in comboPairs:
@@ -175,8 +181,6 @@ def _processMathOne(self, other, funct):
             v2 = other.get(k)
             v = funct(v1, v2)
             kerning[k] = v
-        g1 = self.groups()
-        g2 = other.groups()
         if g1 == g2 or not g1 or not g2:
             groups = g1 or g2
         else:
diff --git a/Lib/fontMath/test/test_mathKerning.py b/Lib/fontMath/test/test_mathKerning.py
index e7fdcb0..183fdca 100644
--- a/Lib/fontMath/test/test_mathKerning.py
+++ b/Lib/fontMath/test/test_mathKerning.py
@@ -115,7 +115,37 @@ def test_copy(self):
         obj2 = obj1.copy()
         self.assertEqual(sorted(obj1.items()), sorted(obj2.items()))
 
-    def test_add(self):
+    def test_add_different_groups_strict(self):
+        kerning1 = {
+            ("A", "A"): 1,
+            ("B", "B"): 1,
+            ("NotIn2", "NotIn2"): 1,
+            ("public.kern1.NotIn2", "C"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups1 = {
+            "public.kern1.NotIn1": ["C"],
+            "public.kern1.D": ["D", "H"],
+            "public.kern2.D": ["D", "H"],
+        }
+        kerning2 = {
+            ("A", "A"): -1,
+            ("B", "B"): 1,
+            ("NotIn1", "NotIn1"): 1,
+            ("public.kern1.NotIn1", "C"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups2 = {
+            "public.kern1.NotIn2": ["C"],
+            "public.kern1.D": ["D", "H"],
+            "public.kern2.D": ["D", "H"],
+        }
+        with self.assertRaises(ValueError):
+            obj = MathKerning(kerning1, groups1, strictGroups=True) + MathKerning(kerning2, groups2)
+        with self.assertRaises(ValueError):
+            obj = MathKerning(kerning1, groups1) + MathKerning(kerning2, groups2, strictGroups=True)
+
+    def test_add_different_groups(self):
         kerning1 = {
             ("A", "A"): 1,
             ("B", "B"): 1,
@@ -195,7 +225,37 @@ def test_add_same_groups(self):
             obj.groups()["public.kern2.D"],
             ['D', 'H'])
 
-    def test_sub(self):
+    def test_sub_different_groups_strict(self):
+        kerning1 = {
+            ("A", "A"): 1,
+            ("B", "B"): 1,
+            ("NotIn2", "NotIn2"): 1,
+            ("public.kern1.NotIn2", "C"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups1 = {
+            "public.kern1.NotIn1": ["C"],
+            "public.kern1.D": ["D", "H"],
+            "public.kern2.D": ["D", "H"],
+        }
+        kerning2 = {
+            ("A", "A"): -1,
+            ("B", "B"): 1,
+            ("NotIn1", "NotIn1"): 1,
+            ("public.kern1.NotIn1", "C"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups2 = {
+            "public.kern1.NotIn2": ["C"],
+            "public.kern1.D": ["D"],
+            "public.kern2.D": ["D", "H"],
+        }
+        with self.assertRaises(ValueError):
+            obj = MathKerning(kerning1, groups1, strictGroups=True) - MathKerning(kerning2, groups2)
+        with self.assertRaises(ValueError):
+            obj = MathKerning(kerning1, groups1) - MathKerning(kerning2, groups2, strictGroups=True)
+
+    def test_sub_different_groups(self):
         kerning1 = {
             ("A", "A"): 1,
             ("B", "B"): 1,
@@ -235,6 +295,40 @@ def test_sub(self):
             obj.groups()["public.kern2.D"],
             ['D', 'H'])
 
+    def test_sub_same_groups(self):
+        kerning1 = {
+            ("A", "A"): 1,
+            ("B", "B"): 1,
+            ("NotIn2", "NotIn2"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups1 = {
+            "public.kern1.D": ["D", "H"],
+            "public.kern2.D": ["D", "H"],
+        }
+        kerning2 = {
+            ("A", "A"): -1,
+            ("B", "B"): 1,
+            ("NotIn1", "NotIn1"): 1,
+            ("public.kern1.D", "public.kern2.D"): 1,
+        }
+        groups2 = {
+            "public.kern1.D": ["D"],
+            "public.kern2.D": ["D", "H"],
+        }
+        obj = MathKerning(kerning1, groups1) - MathKerning(kerning2, groups2)
+        self.assertEqual(
+            sorted(obj.items()),
+            [(('A', 'A'), 2),
+             (('NotIn1', 'NotIn1'), -1),
+             (('NotIn2', 'NotIn2'), 1)])
+        self.assertEqual(
+            obj.groups()["public.kern1.D"],
+            ['D', 'H'])
+        self.assertEqual(
+            obj.groups()["public.kern2.D"],
+            ['D', 'H'])
+
     def test_mul(self):
         kerning = {
             ("A", "A"): 0,