Motivated by our meta-analytic dataset involving survival rates after treatment for critical leg ischemia, we develop and apply a new multivariate model for the meta-analysis of study level survival data at multiple times. Our data set involves 50 studies that provide mortality rates at up to seven time points, which we model simultaneously, and we compare the results to those obtained from standard methodologies. Our method uses exact binomial within-study distributions and enforces the constraints that both the study specific and the overall mortality rates must not decrease over time. We directly model the probabilities of mortality at each time point, which are the quantities of primary clinical interest. We also present "I[superscript 2]" statistics that quantify the impact of the between-study heterogeneity, which is very considerable in our data set.