diff --git a/Tests/images/16bit.r.tif b/Tests/images/16bit.r.tif
new file mode 100644
index 00000000000..0f3996e95eb
Binary files /dev/null and b/Tests/images/16bit.r.tif differ
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index d8d5753f6db..a94e4dc337e 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -225,6 +225,15 @@ def test_big_endian(self):
         assert b[0] == ord(b"\x01")
         assert b[1] == ord(b"\xe0")
 
+    def test_16bit_r(self):
+        with Image.open("Tests/images/16bit.r.tif") as im:
+            assert im.getpixel((0, 0)) == 480
+            assert im.mode == "I;16"
+
+            b = im.tobytes()
+        assert b[0] == ord(b"\xe0")
+        assert b[1] == ord(b"\x01")
+
     def test_16bit_s(self):
         with Image.open("Tests/images/16bit.s.tif") as im:
             im.load()
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 3b70512605f..4165fabfcb0 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -175,6 +175,7 @@
     (II, 1, (1,), 1, (12,), ()): ("I;16", "I;12"),
     (II, 1, (1,), 1, (16,), ()): ("I;16", "I;16"),
     (MM, 1, (1,), 1, (16,), ()): ("I;16B", "I;16B"),
+    (II, 1, (1,), 2, (16,), ()): ("I;16", "I;16R"),
     (II, 1, (2,), 1, (16,), ()): ("I", "I;16S"),
     (MM, 1, (2,), 1, (16,), ()): ("I", "I;16BS"),
     (II, 0, (3,), 1, (32,), ()): ("F", "F;32F"),
diff --git a/src/libImaging/Unpack.c b/src/libImaging/Unpack.c
index 4f9838fa8f6..fc7568a2c4b 100644
--- a/src/libImaging/Unpack.c
+++ b/src/libImaging/Unpack.c
@@ -1124,6 +1124,16 @@ unpackI16N_I16(UINT8 *out, const UINT8 *in, int pixels) {
         tmp += 2;
     }
 }
+static void
+unpackI16R_I16(UINT8 *out, const UINT8 *in, int pixels) {
+    int i;
+    for (i = 0; i < pixels; i++) {
+        out[0] = BITFLIP[in[0]];
+        out[1] = BITFLIP[in[1]];
+        in += 2;
+        out += 2;
+    }
+}
 
 static void
 unpackI12_I16(UINT8 *out, const UINT8 *in, int pixels) {
@@ -1731,6 +1741,8 @@ static struct {
     {"I;16L", "I;16N", 16, unpackI16N_I16},  // LibTiff native->image endian.
     {"I;16B", "I;16N", 16, unpackI16N_I16B},
 
+    {"I;16", "I;16R", 16, unpackI16R_I16},
+
     {"I;16", "I;12", 12, unpackI12_I16},  // 12 bit Tiffs stored in 16bits.
 
     {NULL} /* sentinel */