We consider the issue of Block Bootstrap methods in processes that exhibit strong dependence. The main difficulty is to transform the series in such way that implementation of these techniques can provide an accurate approximation to the true distribution of the test statistic under consideration. The bootstrap algorithm we suggest consists of the following operations: given xt ~ I(d0), 1) estimate the long memory parameter and obtain dˆ, 2) difference the series dˆ times, 3) apply the block bootstrap on the above and finally, 4) cumulate the bootstrap sample dˆ times. Repetition of steps 3 and 4 for a sufficient number of times, results to a successful estimation of the distribution of the test statistic. Furthermore, we establish the asymptotic validity of this method. Its finite-sample properties are investigated via Monte Carlo experiments and the results indicate that it can be used as an alternative, and in most of the cases to be preferred than the Sieve AR bootstrap for fractional processes.