The standard exponential backoff mechanism and many proposed schemes for 802.11 wireless LAN behave adaptively to transmission failures, which occur by two causes: collision and channel noise. However, in 802.11 wireless LAN, a station cannot know the cause of a transmission failure, thus the adaptive schemes assume the ideal situation in which all transmission failures occur by one cause. Therefore, they may behave erroneously in the real world where transmission failures occur by both causes. In this paper, we propose a novel scheme to detect collision, which can help 802.11 and many adaptive schemes to differentiate the causes of transmission failures. In the proposed scheme, stations exchange transmission time information when transmission failures occur. The proposed scheme can detect collision accurately with low bandwidth overhead and it can be implemented without modifying the physical layer of existing wireless LAN devices. In addition, we model the bandwidth overhead of the proposed scheme mathematically. In the simulation, we show that the performance of the automatic rate fallback link adaptation algorithm can be improved by more than 400% with the proposed scheme when the number of stations in a basic service set is 10.