To the mass public, Bitcoin is well known since its creation by its extreme volatility. However, Bitcoin’s declining fluctuations since the start 2015 has revived our attention to assess whether there is a coming Bitcoin market phase. Using an optimal GARCH model on daily data, we show that the volatility of Bitcoin price decreases notably when comparing the periods [December 2010-June 2015] and [January 2015-June 2015]. During the first interval, the Threshold- GARCH estimates reveal that there is a great duration of persistence and thus tends to follow a long memory process. For the second period, the chosen specification (ExponentialGARCH) displays less volatility persistence. Despite this remarkable volatility’s decrease, we cannot argue that Bitcoin market is mature, since the degree of asymmetry remains strong; Specifically, Bitcoin is likely to be driven by negative rather than positive shocks.