The study of S-box properties relations is an interesting problem. In this work we develop and apply a local search method to create trajectories over S-box space. These trajectories shows the existence of an strong linear correlation between confusion coefficient variance, Transparency Order, Modified Transparency Order and Revised Transparency Order, under the Hamming Weight model. When the values of Confusion Coefficient Variance increases then the values of Transparency Order, the values of Modified Transparency Order beta zero, and the values of Revised Transparency Order beta zero, decreases, reflecting the same theoretical resistance against to Side-Channel Attacks by power consumption. As far as we know, it is the first time that Local Search trajectories are used to discover relations between cryptography properties.