We present a new technique for computing the transitive closure of a regular relation characterized by a finite-state transducer. The construction starts from the original transducer, and repeatedly adds new transitions which are compositions of currently existing transitions. Furthermore, we define an equivalence relation which we use to merge states of the transducer during the construction. The equivalence relation can be determined by a simple local check, since it is syntactically characterized in terms of "columns" that label constructed states. This makes our algorithm both simpler to present and more efficient to implement, compared to existing approaches. We have implemented a prototype and carried out verification of a number of parameterized protocols.