Abstract: In order to execute a parallel program Pp on a parallel machine PM, we must determine an allocation function which assigns Pp operations to PM processors, such that the execution time of Pp is minimum. As this problem is known to be NP-complete, a lot of alternative approaches have been proposed in the literature. We refer to load balancing (LB) approaches, ie. to mapping algorithms which determine allocation function by uniformly distributing the computational load among PM processors. Through a simple example we show that internode precedence relations (IPR) cannot be neglected in LB algorithms when we want to achieve high speed up. As far as we know, LB algorithms do not consider IPR, so we present a new LB algorithm which determines an allocation of Pp on PM respecting IPR. We compare the parallel execution times achievable through the presented algorithm with the ones given by the mapping algorithm described in (Bultan and Aykanar, 1992); comparisons, based on actual executions of Pp with different sizes and granularities, show that the presented algorithm gives performance improvements varying from 6% to 76%.