diff --git a/libavcodec/cbs_mpeg2.c b/libavcodec/cbs_mpeg2.c
index c529038fd9..52252093b3 100644
--- a/libavcodec/cbs_mpeg2.c
+++ b/libavcodec/cbs_mpeg2.c
@@ -170,27 +170,41 @@ static int cbs_mpeg2_split_fragment(CodedBitstreamContext *ctx,
     CodedBitstreamUnitType unit_type;
     uint32_t start_code = -1;
     size_t unit_size;
-    int err, i;
+    int err, i, final = 0;
 
     start = avpriv_find_start_code(frag->data, frag->data + frag->data_size,
                                    &start_code);
+    if (start_code >> 8 != 0x000001) {
+        // No start code found.
+        return AVERROR_INVALIDDATA;
+    }
+
     for (i = 0;; i++) {
         unit_type = start_code & 0xff;
 
+        if (start == frag->data + frag->data_size) {
+            // The last four bytes form a start code which constitutes
+            // a unit of its own.  In this situation avpriv_find_start_code
+            // won't modify start_code at all so modify start_code so that
+            // the next unit will be treated as the last unit.
+            start_code = 0;
+        }
+
         end = avpriv_find_start_code(start--, frag->data + frag->data_size,
                                      &start_code);
 
         // start points to the byte containing the start_code_identifier
-        // (or to the last byte of fragment->data); end points to the byte
+        // (may be the last byte of fragment->data); end points to the byte
         // following the byte containing the start code identifier (or to
         // the end of fragment->data).
-        if (end == frag->data + frag->data_size) {
-            // We didn't find a start code, so this is the final unit.
-            unit_size = end - start;
-        } else {
+        if (start_code >> 8 == 0x000001) {
             // Unit runs from start to the beginning of the start code
             // pointed to by end (including any padding zeroes).
             unit_size = (end - 4) - start;
+        } else {
+           // We didn't find a start code, so this is the final unit.
+           unit_size = end - start;
+           final     = 1;
         }
 
         err = ff_cbs_insert_unit_data(ctx, frag, i, unit_type, (uint8_t*)start,
@@ -198,7 +212,7 @@ static int cbs_mpeg2_split_fragment(CodedBitstreamContext *ctx,
         if (err < 0)
             return err;
 
-        if (end == frag->data + frag->data_size)
+        if (final)
             break;
 
         start = end;