diff --git a/Tests/test_lib_pack.py b/Tests/test_lib_pack.py
index 4a7e1f844..432754088 100644
--- a/Tests/test_lib_pack.py
+++ b/Tests/test_lib_pack.py
@@ -344,10 +344,15 @@ class TestLibUnpack(PillowTestCase):
         self.assert_unpack("I;16", "I;16", 2, 0x0201, 0x0403, 0x0605)
         self.assert_unpack("I;16B", "I;16B", 2, 0x0102, 0x0304, 0x0506)
         self.assert_unpack("I;16L", "I;16L", 2, 0x0201, 0x0403, 0x0605)
-        self.assert_unpack("I;16", "I;16N", 2, 0x0201, 0x0403, 0x0605)
-        self.assert_unpack("I;16B", "I;16N", 2, 0x0201, 0x0403, 0x0605)
-        self.assert_unpack("I;16L", "I;16N", 2, 0x0201, 0x0403, 0x0605)
         self.assert_unpack("I;16", "I;12", 2, 0x0010, 0x0203, 0x0040, 0x0506)
+        if sys.byteorder == 'little':
+            self.assert_unpack("I;16", "I;16N", 2, 0x0201, 0x0403, 0x0605)
+            self.assert_unpack("I;16B", "I;16N", 2, 0x0201, 0x0403, 0x0605)
+            self.assert_unpack("I;16L", "I;16N", 2, 0x0201, 0x0403, 0x0605)
+        else:
+            self.assert_unpack("I;16", "I;16N", 2, 0x0102, 0x0304, 0x0506)
+            self.assert_unpack("I;16B", "I;16N", 2, 0x0102, 0x0304, 0x0506)
+            self.assert_unpack("I;16L", "I;16N", 2, 0x0102, 0x0304, 0x0506)
 
     def test_value_error(self):
         self.assertRaises(ValueError, self.assert_unpack, "L", "L", 0, 0)