Concolic testing tools can automatically generate test cases. However, there is a scope to increase the coverage achieved. Pair-wise testing is a prominent black-box testing method. We propose to combine ideas from these two techniques to enhance the code coverage. We have carried out experimental studies to evaluate the effectiveness of our approach. Our experimental results show that on an average our approach achieves 3.27%, 2.94%, and 6.22% improvements in condition coverage, decision coverage, and MC/DC respectively over a traditional concolic tester. Further, on an average of 4.36% improvement in mutation score is achieved.