In order to find gene regulatory networks from microarray data, it is important to first find direct regulatory relationships between pairs of genes. We propose a new method for finding potential regulatory relationships between pairs of genes from microarray time series data and apply it to expression data for cell-cycle related genes in yeast. We compare our algorithm, dubbed the event method, with the earlier correlation method and the edge detection method by Filkov et al. When tested on known transcriptional regulation genes, all three methods are able to find similar numbers of true positives. The results indicate that our algorithm is able to identify true positive pairs that are different from those found by the two other methods. We also compare the correlation and the event methods using synthetic data and find that typically, the event method obtains better results.