  In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra
modules over the Schr\"{o}dinger-Virasoro algebra are studied. It is proved
that there are only two classes conjugate-linear anti-involutions over the
Schr\"{o}dinger-Virasoro algebra. The main result of this paper is that a
unitary Harish-Chandra module over the Schr\"{o}dinger-Virasoro algebra is
simply a unitary Harish-Chandra module over the Virasoro algebra.
