A one-sample nonparametric test is proposed which sequentially examines the values of the Wilcoxon signed-rank statistic. The test rejects the null hypothesis of symmetry about zero if for anynbetween 1 andNthe Wilcoxon signed-rank statistic forX1, …,Xndiffers from its null mean by |z|aNstandard deviations; otherwise the null hypothesis is accepted. The critical constant |z|aNis determined by Monte Carlo sampling.