If $R=\bmatrix H\\ B\endbmatrix$, where $H=H^*$, we find a pseudo-inverse form of all solutions $W=W^*$, such that $\|A\|=\|R\|$, where $A=\bmatrix H&B^*\\ B& W\endbmatrix$ and $\|H\|\leq\|R\|$. In this paper we extend well-known results in a finite dimensional setting, proved by Dao-Sheng Zheng [15]. Thus, a pseudo inverse form of solutions of the Davis-Kahan-Weinberger theorem is established.