In grid workflow systems, existing typical checkpoint selection strategies, which are used to select checkpoints for verifying fixed-time constraints at run-time execution stage, are not effective and/or efficient for fixed-time constraint verification because they often ignore some necessary checkpoints and select some unnecessary checkpoints. To improve such status, in this paper, we develop a new checkpoint selection strategy. Specifically, we first address a new concept of minimum proportional time redundancy which can be used to tolerate certain time deviation incurred by abnormal grid workflow execution. Then, we discuss relationships between minimum proportional time redundancy and fixed-time constraint consistency. Based on the relationships, we present our new strategy. With the strategy, we can avoid the omission of necessary checkpoints and the selection of excess unnecessary checkpoints. Consequently, our strategy is more effective and efficient for fixed-time constraint verification than the existing typical strategies. The final evaluation further demonstrates this result.