  This work gains a sharp sufficient condition on the block restricted isometry
property for the recovery of sparse signal. Under the certain assumption, the
signal with block structure can be stably recovered in the present of noisy
case and the block sparse signal can be exactly reconstructed in the noise-free
case. Besides, an example is proposed to exhibit the condition is sharp. As
byproduct, when $t=1$, the result improves the bound of block restricted
isometry constant $\delta_{s|\mathcal{I}}$ in Lin and Li (Acta Math. Sin. Engl.
Ser. 29(7): 1401-1412, 2013).
