  We prove that each non-metrizable sequential rectifiable space $X$ of
countable $cs^*$-character contains a clopen rectifiable submetrizable
$k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces
homeomorphic to clopen subspaces of $H$. This implies that each sequential
rectifiable space with countable $cs^*$-character either is metrizable or else
is a topological sum of submetrizable $k_\omega$-spaces. Consequently, $X$ is
submetrizable and paracompact. This answers a question of Lin and Shen posed in
2011.
