This paper presents an algorithm which transform a generalized left-linear recursion into more efficient rules,and shows the correctness of the given algorithm. A generalized left-linear recursion contains one or more IDB predicates and its definition is essentially generalized from that of left-linear recursions. As the algorithm for the evaluation of left - linear recursions, the algorithm we present here follows the magic-sets paradigm of a rewriting phase followed by semi -naive bottom-up evaluation. The efficinecy of the transformed rules is also discussed in this paper.