Improvement to straightforward implementation of a statistically inspired modification of the partial least squares (SIMPLS) algorithm has been suggested for the case of many explanatory variables, X, and fewer objects, N. The improved SIMPLS algorithm, the SIMPLS algorithm and PLS kernel algorithm have been compared in terms of speed. The results reveal that improvement on the SIMPLS algorithm makes the algorithm much faster than the SIMPLS algorithm. Moreover, the improved algorithm is competitive with or even faster than the PLS kernel algorithm under the considered cases.