  We show that Penkov's approach to a superanalog of Borel-Bott-Weil theorem
for $G=GL(m|n)$ over a field of zero characteristic can be extended for a
perfect field of arbitrary odd characteristic. We also prove some partial
version of Kempf's vanishing theorem and characteristic free formula for Euler
characteristic $\chi(B, \lambda^{\epsilon})$, where $B$ is a Borel subgroup of
$G$.
