According to the Hypothesis of Efficient Market -HME, proposed by Fama (1970), in its weak form, an investor doesn't get to predict the stock returns based on historical returns and thus doesn't get abnormal returns in a consistent way. This paper is concerned verifying HME, in the weak form, in the Brazilian stock market by the analysis of fifty more negotiated stocks in BOVESPA since 2000 until 2007. The methodology was used based in the ARIMA models of time series and serial correlation tests of returns to prove or not the random behavior of the stock returns. The results had shown that Brazilian capital market did not evidence characteristics of an efficient market, in the weak form, in the considered period.The brazilian stock market of the new millennium: an efficiency test 221 JEGADEESH, N.; TITMAN, S. Returns to buying winners and selling losers: implications for stock market efficiency.The brazilian stock market of the new millennium: an efficiency test 231