  We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363
(1989)] of a full set of mutually unbiased bases in a complex vector space of
dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character
vectors of the cyclic group $G$ of order $p$. This form may be useful in
explicitly writing down mutually unbiased bases for $N=p^r$.
