A new implementation of Block Adaptive filter in frequency domain is presented in this paper. Block digital filtering involves the calculation of a block or finite set of filter out put from a block of input values. A fast convergence algorithm of block adaptive filter is developed using Gordar theory and compared with the performance results of Satio algorithm and BLMS algorithm. Form the result we can be shown that the convergence state of given algorithm is not only faster than BLMS algorithm but also the resulting convergence error is less than the convergence error of Satio algorithm.