The steady state performance of gradient-based algorithms for adaptive IIR filtering is largely dependent on the gradient estimates. Due to the recursive nature of the IIR filtering, such gradient estimates are difficult to determine. In an attempt to remedy this problem, this paper presents a new adaptive procedure which provides more accurate estimates of the gradients. The result is a new block gradient-based adaptive algorithm. The input signals are divided into data blocks and the coefficients are kept constant within every block. For each block of data the gradients are evaluated and subsequently used to update the coefficients for the next block. In other words, the proposed algorithm updates the coefficients on block by block basis. In contrast with the conventional Recursive Prediction Error (RPE) algorithm, the proposed approach is characterized by improved the steady state error and less computational complexity.