Null hypothesis for Wilcoxon Signed Rank test

Hi, I am using the Wilcoxon Signed Rank test to examine changes in a groups scores from time 1 to time 2. The distribution of score changes is non-normal. Scores can range from 1 - 5, and the median score is 2 at both time 1 and time 2. However, the test still shows a significant difference (z = -2.53, p = 0.001 one tailed exact test). Given that the null hypothesis is that there is no difference between median scores from time 1 to time 2, how can there be a statistically significant change if the median is the same? Does the test (due to the exclusion of certain pairs of data) go beyond this? Or have I made a mistake?