  A gyrogroup is a structure constituting from a non-empty set and a binary
operation such that satisfying the left identity, and left inverse conditions,
and also has the associative-like law said to be left gyroassociativity and
left loop property. In this paper, we propose a method for constructing new
gyrogroups of order $2^n$ by a cyclic 2-group that is $\mathbb{Z}_{2^n}$, where
$n\geq 3$.
