In this study, the weak efficiency of the Istanbul Stock Exchange (1SE) National 100 Price Index was investigated using weekly data between 1986-2002 period employing Random Walk Process. As an alternative to the previous studies concerning the weak efficiency of ISE, stochastic unit root analysis was performed for price changes. Secondly, roots for each time point were estimated by Kalman Filter Method. Thus, weak efficiency of the ISE was determined for each time point instead of a periodic determination. Moreover, with the exception of 1987, ISE data was not seen to be weak in efficiency.