Digital predistortion (DPD) is a technique that aims at linearizing power amplifiers and thus allows energy efficiency improvements. However, this technique requires, wideband and high dynamic range analog-to-digital converters (ADC) and usually large computational resources. Subband digitization with subband DPD algorithm have been proposed to relax the design constraints of the feedback path ADC and the digital processing unit. We present in this article a subsampled RLS-based subband DPD algorithm. We show that the gain in terms of number of multiplications and/or additions per second (MAC/s), between the conventional wideband approach and the subsampled algorithm, tends to the number of subbands. Simulations show that the convergence speed by RLS iteration of the subsampled algorithm is maintained. Therefore, the subsampled algorithm converges with the same number of iterations as the conventional wideband approach. After convergence, the residual mean-square-error (MSE) is approximately -76dB for the conventional wideband algorithm and -70dB for the proposed algorithm.