  Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the
8 multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$,
$k\in\{-1, 1\}$. Define a new multiplication on $G\times C_2$ by assigning one
of the above 8 multiplications to each quarter
$(G\times\{i\})\times(G\times\{j\})$, for $i$, $j\in C_2$. We describe all
situations in which the resulting quasigroup is a Bol loop. This paper also
corrects an error in P. Vojt\v{e}chovsk\'y: On the uniqueness of loops
$M(G,2)$.
