An affine-invariant signed sum test based on interdirections is proposed for the one-sample multivariate location problem. The test proposed, including the two-sided univariate Wilcoxon signed-rank test as a special case, is somewhat like applying the interdirection sign test to the sums of pairs of observed vectors. The proposed statistic is shown to have a limiting x²_p null distribution when the underlying distribution is elliptically symmetric. In addition, the asymptotic distribution of the statistic under certain contiguous alternatives is obtained for elliptically symmetric distributions with a particular density function form. Comparisons made between the proposed test and Hotelling's T² via Pitman asymptotic relative efficiencies show the signed sum test performs better than Hotelling's T² when the underlying distribution is heavy-tailed.