  We prove that for any $\alpha\in[0,\omega_1)$ there exists a strongly
separately continuous function $f:\ell_\infty\to [0,1]$ such that $f$ belongs
to the $(\alpha+1)$'th /$(\alpha+2)$'th/ Baire class and does not belong to the
$\alpha$'th Baire class if $\alpha$ is finite /infinite/.
