The purpose of this paper is to test the hypothesis of the financial market efficiency. Thus, the evolution of the daily informational efficiency is measured for Tunisian stock market index (TUNINDEX) by using the Shannon entropy, over the period [2007 ñ2009]. After that, a logit model is applied in order to study the relationship between efficiency and probability of the financial crash. The main results seem to confirm the negative relationship between the probability of crash and the efficiency.