diff --git a/requests/utils.py b/requests/utils.py
index 4def3dba..47325090 100644
--- a/requests/utils.py
+++ b/requests/utils.py
@@ -714,7 +714,7 @@ def guess_json_utf(data):
     # easy as counting the nulls and from their location and count
     # determine the encoding. Also detect a BOM, if present.
     sample = data[:4]
-    if sample in (codecs.BOM_UTF32_LE, codecs.BOM32_BE):
+    if sample in (codecs.BOM_UTF32_LE, codecs.BOM_UTF32_BE):
         return 'utf-32'     # BOM included
     if sample[:3] == codecs.BOM_UTF8:
         return 'utf-8-sig'  # BOM included, MS style (discouraged)
diff --git a/tests/test_utils.py b/tests/test_utils.py
index c92c7323..8d5ade9c 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -274,6 +274,17 @@ class TestGuessJSONUTF:
     def test_bad_utf_like_encoding(self):
         assert guess_json_utf(b'\x00\x00\x00\x00') is None
 
+    @pytest.mark.parametrize(
+        ('encoding', 'expected'), (
+            ('utf-16-be', 'utf-16'),
+            ('utf-16-le', 'utf-16'),
+            ('utf-32-be', 'utf-32'),
+            ('utf-32-le', 'utf-32')
+        ))
+    def test_guess_by_bom(self, encoding, expected):
+        data = u'\ufeff{}'.encode(encoding)
+        assert guess_json_utf(data) == expected
+
 
 USER = PASSWORD = "%!*'();:@&=+$,/?#[] "
 ENCODED_USER = compat.quote(USER, '')