For many infectious agents, seroprevalence rate is low but has serious consequences and must therefore be kept out of donated blood supplies. However, screening to ensure the safety of blood supplies has an associated very high cost. For example, in blood banks, detection of all the harmful items in a large number of samples is an expensive and tedious process. The laboratory and statistical approaches to obtain significant savings by the pooling method were discussed from 1943, recently, there have been further discussions of pooling sera as a means to determining the HIV seroprevalence rate in the general population or the weed out all HIV-positive individuals in blood screening. Here we describe a simple mathematical method to weed out all HIV, and HCV seropositive units. The method is designed to maximize possible savings. Two examples illustrate the application of this method in determining the number to be pooled in each stage, and the resulting savings. When the prevalence rate is lower than 2 percent. our method offers savings of over 80 percent.