In this work, a novel algorithm, called the signed regressor least mean fourth (SRLMF) adaptive algorithm, that reduces the computational cost and complexity while maintaining good performance is presented. Expressions are derived for the steady-state excess-mean-square error (EMSE) of the SRLMF algorithm in a stationary environment. Moreover, the tracking analysis of the proposed algorithm is also provided in a nonstationary environment. Computer simulations are carried out to corroborate the theoretical findings. It is shown that there is a good match between the theoretical and simulation results. It is also shown that the SRLMF algorithm has no performance degradation when compared with the least mean fourth (LMF) algorithm.