  We prove that if $X$ is a paracompact connected space and $Z=\prod_{s\in
S}Z_s$ is a product of a family of equiconnected metrizable spaces endowed with
the box topology, then for every Baire-one map $g:X\to Z$ there exists a
separately continuous map $f:X^2\to Z$ such that $f(x,x)=g(x)$ for all $x\in
X$.
