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In grid workflow systems, temporal correctness is critical to assure the timely completion of grid workflow execution. To monitor and control the temporal correctness, fixed-time constraints are often assigned to a grid workflow and then verified. A checkpoint selection strategy is used to select checkpoints along grid workflow execution for verifying fixed-time constraints. The problem of existing representative strategies is that they do not differentiate fixed-time constraints as once a checkpoint is selected, they verify all fixed-time constraints. However, these checkpoints do not need to be taken for those constraints whose consistency can be deduced from others. The corresponding verification of such constraints is consequently unnecessary and can severely impact the efficiency of overall temporal verification. To address the problem, in this paper, we develop a new temporal dependency based checkpoint selection strategy which can select checkpoints according to different fixed-time constraints. With our strategy, the corresponding unnecessary verification can be avoided. The comparison and experimental simulation further demonstrate that our new strategy can improve the efficiency of overall temporal verification significantly over the existing representative strategies.