The study reexamines the issue of informational efficiency of Bitcoin using data at different frequencies (15, 30, 60 and 120 min and daily data). In particular, we test the martingale hypothesis in Bitcoin returns using different variance ratio tests. We also examine the evolution of informational efficiency of Bitcoin using non-overlapping and overlapping moving window analysis. The study provides evidence of the presence of informational inefficiency in the Bitcoin market at higher frequency levels. The daily Bitcoin returns which appear to be following a memory-less stochastic process are in fact otherwise when we move to the higher frequencies of Bitcoin prices.