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Long impulse response system identification presents two challenges for standard normalized least mean square (NLMS) filtering method: heavy computational load and slow convergence. When the response is sparse, partial update algorithms can reduce the computational complexity, but most often at the expense of performance. This paper discusses the tap selection rule for partial update NLMS algorithm in the case of white Gaussian input. We consider output mean square error (MSE) minimization based on gradient analysis and propose an algorithm that switches tap selection criterion between the one based on filter coefficient magnitudes and the one based on input magnitudes. We show that for identifying sparse systems, the new algorithm can outperform standard NLMS significantly with a reduced computational load.