  We consider an initial boundary value problem in a bounded domain $\Omega$
over a time interval $(0, T)$ for a time-fractional wave equation where the
order of the fractional time derivative is between $1$ and $2$ and the spatial
elliptic operator has time-independent coefficients and is not necessarily
symmetric. We prove that if for arbitrarily chosen subdomain $\omega\subset
\Omega$ and $T>0$, a solution to the problem vanishes in $\omega \times (0,T)$,
then $u=0$ in $\Omega \times (0, T)$. The uniqueness does not require any
geometric condition on $\omega$.
