Mann–Kendall (MK) test for trend detection must be modified when the data are serially correlated, to prevent the detection of false trends. Various approaches are developed for this purpose, such as prewhitening, trend‐free prewhitening, variance correction and block bootstrap. Each method has its own Type I and Type II errors. In this study, the errors of block bootstrapping MK test are estimated by a simulation study and compared with other methods. Optimal block length that minimizes the Type I error is determined as function of sample size and autocorrelation coefficient. It is shown that the power of block bootstrapping MK test is comparable with those of other modified MK tests. These tests are applied to some annual streamflow series with trend recorded in Turkish rivers, and their powers are compared. A modified form of the trend‐free prewhitening procedure is proposed that has a smaller Type I error. Copyright © 2011 John Wiley & Sons, Ltd.