  In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(\lambda),L_n(\mu))$,
where GL(n) is the general linear group of degree $n$ over an algebraically
closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are
rational irreducible GL(n)-modules with highest weights $\lambda$ and $\mu$
respectively, the restriction of $L_n(\lambda)$ to any Levi subgroup of GL(n)
is semisimple, $\lambda$ is a $p$-restricted weight and $\mu$ does not strictly
dominate $\lambda$.
