A multivariate nonparametric statistic is proposed for testing independence among many vectors. The statistic is an extension of the interdirection quadrant statistic introduced by Gieser and Randles for the case of two vectors. The proposed statistic is affine-invariant under a class of nonsingular linear transformations and has an asymptotc chi-square distribution under the null hypothesis of independence when each vector has an elliptically symmetric distribution. It is shown that the proposed test performs better than other tests in the literature when the underlying distributions are heavy-tailed