In this paper, we will prove a $L^2$-concentration result of
Zakharov system in space dimension two, with initial data
$(u_0,n_0,n_1)\in H^s\times L^2\times H^{-1}$ ($\frac
{1 2}{1 3} < s < 1$), when blow up of the solution happens, by resonant
decomposition and I-method, which is an improvement of [13].