diff --git a/libavcodec/hevc_parser.c b/libavcodec/hevc_parser.c
index 87270cffb4..99a4272fad 100644
--- a/libavcodec/hevc_parser.c
+++ b/libavcodec/hevc_parser.c
@@ -278,6 +278,8 @@ static int hevc_find_frame_end(AVCodecParserContext *s, const uint8_t *buf,
             (nut >= 41 && nut <= 44) || (nut >= 48 && nut <= 55)) {
             if (pc->frame_start_found) {
                 pc->frame_start_found = 0;
+                if (!((pc->state64 >> 6 * 8) & 0xFF))
+                    return i - 6;
                 return i - 5;
             }
         } else if (nut <= HEVC_NAL_RASL_R ||
@@ -288,6 +290,8 @@ static int hevc_find_frame_end(AVCodecParserContext *s, const uint8_t *buf,
                     pc->frame_start_found = 1;
                 } else { // First slice of next frame found
                     pc->frame_start_found = 0;
+                    if (!((pc->state64 >> 6 * 8) & 0xFF))
+                        return i - 6;
                     return i - 5;
                 }
             }
diff --git a/tests/fate/hevc.mak b/tests/fate/hevc.mak
index b3c6792140..4889ee8237 100644
--- a/tests/fate/hevc.mak
+++ b/tests/fate/hevc.mak
@@ -222,7 +222,7 @@ FATE_HEVC-$(call ALLYES, HEVC_DEMUXER MOV_DEMUXER HEVC_PARSER HEVC_MP4TOANNEXB_B
 fate-hevc-bsf-mp4toannexb: tests/data/hevc-mp4.mov
 fate-hevc-bsf-mp4toannexb: CMD = md5 -i $(TARGET_PATH)/tests/data/hevc-mp4.mov -c:v copy -fflags +bitexact -f hevc
 fate-hevc-bsf-mp4toannexb: CMP = oneline
-fate-hevc-bsf-mp4toannexb: REF = 1873662a3af1848c37e4eb25722c8df9
+fate-hevc-bsf-mp4toannexb: REF = 73019329ed7f81c24f9af67c34c640c0
 
 fate-hevc-skiploopfilter: CMD = framemd5 -skip_loop_filter nokey -i $(TARGET_SAMPLES)/hevc-conformance/SAO_D_Samsung_5.bit -sws_flags bitexact
 FATE_HEVC-$(call FRAMEMD5, HEVC, HEVC, HEVC_PARSER) += fate-hevc-skiploopfilter