We developed a new computational technique called Step-Level Differential Response (SLDR) to identify genetic regulatory relationships. Our technique takes advantages of functional genomics data for the same species under different perturbation conditions, therefore complementary to current popular computational techniques. It can particularly identify "rare" activation/inhibition relationship events that can be difficult to find in experimental results. In SLDR, we model each candidate target gene as being controlled by N binary-state regulators that lead to ≤2N observable states ("step-levels") for the target. We applied SLDR to the study of the GEO microarray data set GSE25644, which consists of 158 different mutant S. cerevisiae gene expressional profiles. For each target gene t, we first clustered ordered samples into various clusters, each approximating an observable step-level of t to screen out the "de-centric" target. Then, we ordered each gene x as a candidate regulator and aligned t to x for the purpose of examining the step-level correlations between low expression set of x (Ro) and high expression set of x (Rh) from the regulator x to t, by finding max f(t, x): |Ro-Rh| over all candidate × in the genome for each t. We therefore obtained activation and inhibitions events from different combinations of Ro and Rh. Furthermore, we developed criteria for filtering out less-confident regulators, estimated the number of regulators for each target t, and evaluated identified top-ranking regulator-target relationship. Our results can be cross-validated with the Yeast Fitness database. SLDR is also computationally efficient with o(N²) complexity. In summary, we believe SLDR can be applied to the mining of functional genomics big data for future network biology and network medicine applications.