Differential evolution (DE) is a class of simple yet powerful evolutionary algorithms for global numerical optimization. Binomial crossover and exponential crossover are two commonly used crossover operators in current popular DE. It is noteworthy that these two operators can only generate a vertex of a hyper-rectangle defined by the mutant and target vectors. Therefore, the search ability of DE may be limited. Orthogonal crossover (OX) operators, which are based on orthogonal design, can make a systematic and rational search in a region defined by the parent solutions. In this paper, we have suggested a framework for using an OX in DE variants and proposed OXDE, a combination of DE/rand/1/bin and OX. Extensive experiments have been carried out to study OXDE and to demonstrate that our framework can also be used for improving the performance of other DE variants.