  A similarity transformation, which brings a particular class of the $N=1$
string to the $N=0$ one, is explicitly constructed. It enables us to give a
simple proof for the argument recently proposed by Berkovits and Vafa. The
$N=1$ BRST operator is turned into the direct sum of the corresponding $N=0$
BRST operator and that for an additional topological sector. As a result, the
physical spectrum of these $N=1$ vacua is shown to be isomorphic to the tensor
product of the $N=0$ spectrum and the topological sector which consists of only
the vacuum. This transformation manifestly keeps the operator algebra.
