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Following the new advances in encryption and network computing, Bitcoin emerged as a private sector system facilitating peer-to-peer exchange via distributed ledgers based on blockchains, driving a transformational change towards a global economy outside the core financial system. The main purpose of this paper is to examine the multifractal properties of the Bitcoin price using high frequency data. The methods used are the wavelet transform modulus maxima and the multifractal detrended fluctuation analysis. The results indicate that Bitcoin exhibits a large degree of multifractality in all examined time intervals, and the main source of multifractality is attributed to the high kurtosis and the fat distributional tails of the series returns.