This work repots results of the convergence analysis of the normalized sign-sign least mean square (NSSLMS) algorithm when the input is real-valued data. The results includes expressions for different parameters, such as the steady-state mean-square error, and the tracking mean-square error. Moreover, the performance of the normalized sign-sign LMS algorithm is compared with that of the sign-sign LMS algorithm. The convergence behavior includes the rate of convergence. Finally, simulation results suggest that the normalized sign-sign LMS algorithm can be used as a good replacement for the sign-sign LMS algorithm as the former algorithm offers comparatively much faster rate of convergence than the latter algorithm.