  A graph $\G$ with a group $H$ of automorphisms acting semiregularly on the
vertices with two orbits is called a {\em bi-Cayley graph} over $H$. When $H$
is a normal subgroup of $\Aut(\G)$, we say that $\G$ is {\em normal} with
respect to $H$. In this paper, we show that every finite group has a connected
normal bi-Cayley graph. This improves Theorem~5 of [M. Arezoomand, B. Taeri,
Normality of 2-Cayley digraphs, Discrete Math. 338 (2015) 41--47], and provides
a positive answer to the Question of the above paper.
