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Exact support recovery of K-group sparse matrices X from the multiple measurement vectors (MMV) model Y = A X arises from many applications and has been extensively studied. In this paper, we investigate the restricted isometry property (RIP) based condition that guarantees exact support recovery of K-group sparse matrices X from the MMV model with greedy block coordinate descent (GBCD) algorithm in K iterations. We show that if A satisfies the RIP with $\delta _{K+1}<1/\sqrt {K+1}$ , then GBCD recovers the support of any K-group sparse matrix X in K iterations. This RIP condition is sharp since GBCD may fail to recover the support of a K-group sparse matrix in K iterations if $\delta _{K+1}\geq 1/\sqrt {K+1}$ . As far as we know, this is the first sharp condition for GBCD. [ABSTRACT FROM AUTHOR]