We first show that if $psi : M_n(B(H)) o M_n (B(H))$ is a $D_n otimes F(H)$-bimodule map, then there is a matrix $A in M_n$ such that $psi = S_A$. Secondly, we show that for an operator space $varepsilon, A in M_n$, the Schur product map $S_A : M_n(varepsilon) o M_n(varepsilon)$ and $phi_A : M_n(varepsilon) o varepsilon$, defined by $phi_A([x_{ij}]) = sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $Vert S_A Vert = Vert S_A Vert_{cb} = Vert A Vert_S, Vert phi_A Vert = Vert phi_A Vert_{cb} = Vert A Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.