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This paper introduces the Modified Adaptive Belief Propagation (m-ABP) algorithm, an innovative method for the turbo decoding of product codes based on BCH component codes. The Adaptive Belief Propagation algorithm of Jiang and Narayanan is simplified by moving the matrix adaptation step outside of the iteration loop, significantly reducing the complexity. Performance in terms of the bit- error-rate (BER) of the novel turbo decoding algorithm is given. Simulation results for the turbo decoding of product codes show that compared to the Chase-Pyndiah algorithm no significant BER deviation is observed while the highly- parallelizable graph-based structure of the algorithm enables high-throughput decoding.