diff --git a/Tests/images/different_transparency.gif b/Tests/images/different_transparency.gif
new file mode 100644
index 000000000..2d36bef9e
Binary files /dev/null and b/Tests/images/different_transparency.gif differ
diff --git a/Tests/images/different_transparency_merged.gif b/Tests/images/different_transparency_merged.gif
new file mode 100644
index 000000000..94d0f53e0
Binary files /dev/null and b/Tests/images/different_transparency_merged.gif differ
diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index 1b2314d51..52d7f035d 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -468,12 +468,25 @@ def test_dispose2_background(tmp_path):
         assert im.getpixel((0, 0)) == 0
 
 
-def test_iss634():
+def test_transparency_in_second_frame():
+    with Image.open("Tests/images/different_transparency.gif") as im:
+        assert im.info["transparency"] == 0
+
+        # Seek to the second frame
+        im.seek(im.tell() + 1)
+        assert im.info["transparency"] == 0
+
+        assert_image_equal_tofile(im, "Tests/images/different_transparency_merged.gif")
+
+
+def test_no_transparency_in_second_frame():
     with Image.open("Tests/images/iss634.gif") as img:
         # Seek to the second frame
         img.seek(img.tell() + 1)
+        assert "transparency" not in img.info
+
         # All transparent pixels should be replaced with the color from the first frame
-        assert img.histogram()[img.info["transparency"]] == 0
+        assert img.histogram()[255] == 0
 
 
 def test_duration(tmp_path):
diff --git a/Tests/test_file_webp_animated.py b/Tests/test_file_webp_animated.py
index 26e903488..25ebffe02 100644
--- a/Tests/test_file_webp_animated.py
+++ b/Tests/test_file_webp_animated.py
@@ -45,12 +45,12 @@ def test_write_animation_L(tmp_path):
             # Compare first and last frames to the original animated GIF
             orig.load()
             im.load()
-            assert_image_similar(im, orig.convert("RGBA"), 25.0)
+            assert_image_similar(im, orig.convert("RGBA"), 32.9)
             orig.seek(orig.n_frames - 1)
             im.seek(im.n_frames - 1)
             orig.load()
             im.load()
-            assert_image_similar(im, orig.convert("RGBA"), 25.0)
+            assert_image_similar(im, orig.convert("RGBA"), 32.9)
 
 
 @pytest.mark.xfail(is_big_endian(), reason="Fails on big-endian")
diff --git a/src/PIL/GifImagePlugin.py b/src/PIL/GifImagePlugin.py
index bf2db4260..2f6d98204 100644
--- a/src/PIL/GifImagePlugin.py
+++ b/src/PIL/GifImagePlugin.py
@@ -173,6 +173,8 @@ class GifImageFile(ImageFile.ImageFile):
         self.palette = copy(self.global_palette)
 
         info = {}
+        frame_transparency = None
+        interlace = None
         while True:
 
             s = self.fp.read(1)
@@ -191,7 +193,7 @@ class GifImageFile(ImageFile.ImageFile):
                     #
                     flags = block[0]
                     if flags & 1:
-                        info["transparency"] = block[3]
+                        frame_transparency = block[3]
                     info["duration"] = i16(block, 1) * 10
 
                     # disposal method - find the value of bits 4 - 6
@@ -249,10 +251,6 @@ class GifImageFile(ImageFile.ImageFile):
                 # image data
                 bits = self.fp.read(1)[0]
                 self.__offset = self.fp.tell()
-                self.tile = [("gif",
-                             (x0, y0, x1, y1),
-                             self.__offset,
-                             (bits, interlace, info.get("transparency", -1)))]
                 break
 
             else:
@@ -278,11 +276,26 @@ class GifImageFile(ImageFile.ImageFile):
         except (AttributeError, KeyError):
             pass
 
-        if not self.tile:
+        if interlace is not None:
+            transparency = -1
+            if frame_transparency is not None:
+                if frame == 0:
+                    self.info["transparency"] = frame_transparency
+                else:
+                    transparency = frame_transparency
+            self.tile = [
+                (
+                    "gif",
+                    (x0, y0, x1, y1),
+                    self.__offset,
+                    (bits, interlace, transparency),
+                )
+            ]
+        else:
             # self.__fp = None
             raise EOFError
 
-        for k in ["transparency", "duration", "comment", "extension", "loop"]:
+        for k in ["duration", "comment", "extension", "loop"]:
             if k in info:
                 self.info[k] = info[k]
             elif k in self.info: