  In this note, we introduce the notion of an unramified strongly cyclic
covering for a cyclic curve, a class that has similar properties to, and
contains, unramified double covers of hyperelliptic curves. We determine
several of their basic properties, extending the theorems in \cite{MR2217998}
to this larger class. In particular, we will write down equations for smooth
affine models, determine when they are isomorphic, and discuss the curves that
they are ramified cyclic covers of.
