Long-term memory of stock markets is a topic that has not received its due attention from academics. Posting the assertion made by Fama, 1970 [1] about markets being efficient, no one can consistently outrun it for a longer duration. Handful of papers checked the efficiency in emerging markets to see if the efficiency proposition held true. Furthering the literature in this study we test for the long-term memory of National Stock Exchange (NSE) index, Nifty and NSE_500 which are a collection of 50 and 500 listed firms respectively in India. The duration of the data for study is roughly eight years over the period from 2006-06-29 to 2012-09-13, a total of 1545 observations. We observe that long-term memory does exist in the context of Indian stock market index.