The weak form of efficient market hypothesis states that the share prices neither have a long memory nor a short memory. Long memory is characterized by non-periodic dependence in a financial time series over a long span of time. This paper examines the long memory of the Indian stock market by examining the daily returns of 60 companies with around 62% of the total market capitalization over a period of five years. The test applied to examine the long memory is Lo’s modified rescaled long range (R/S) test, which is able to derive variance of the time series with a consistent estimate. This test is an improvement over the classical rescaled long range test and is not sensitive to short-term dependence. The results of the study indicate that the returns of only three companies exhibit long-range dependence. The computed test statistics for all other companies were found to be insignificant and showed the absence of long memory, supporting the weak form efficiency of the market.