As more generic drugs become available, the quality, safety, and efficacy of generic drugs have become a public concern. Specifically, drug interchangeability among generic copies of the same brand-name drug is a safety concern. This research proposes a Bayesian method for assessing bioequivalence between two generic copies of the same brand-name drug from two independent $2{ imes}2$ crossover design experiments. Uninformative priors are considered for general use and the posterior distribution of the difference of two generic drug effects is derived from which the highest probability density interval can be evaluated. Examples are presented for illustration.