Let $\mathcal{F}_1, \mathcal{F}_2$ be coherent sheaves over $\mathbb{P}^n_{\mathbb{C}}$ for $n \ge 3$. Now, $\Gamma_*(\mathcal{O}_{\mathbb{P}^n})=\mathbb{C}[X_0,...X_n]$. Denote by $U_0$ the affine scheme $\{X_0 \not=0 \}$. Denote by $D_1$ (resp. $D_2$) the support of $\mathcal{F}_1$ (resp. $\mathcal{F}_2$). Assume that $D_i \cap U_0$ is dense in $D_i$, for $i=1, 2$. Let $\phi_0 \in H^0(U_0,\mathcal{H}om_{\mathbb{P}^n}(\mathcal{F}_1,\mathcal{F}_2)|_{U_0})$ be a morphism. Does there exist a morphism $\phi \in H^0(\mathbb{P}^n,\mathcal{H}om_{\mathbb{P}^n}(\mathcal{F}_1,\mathcal{F}_2))$ such that $\phi|_{U_0}=\phi_0$?