This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems that have constraints on test parameters. Such constraints are common in real-world systems; thus CLA enhances the applicability of locating arrays to practical testing problems. The paper also proposes an algorithm for constructing CLAs. Experimental results show that the proposed algorithm scales to problems of practical sizes.