  We study the series expansion of the tau function of the BKP hierarchy
applying the addition formulae of the BKP hierarchy. Any formal power series
can be expanded in terms of Schur functions. It is known that, under the
condition $\tau(x)\neq0$, a formal power series $\tau(x)$ is a solution of the
KP hierarchy if and only if its coefficients of Schur function expansion are
given by the so called Giambelli type formula. A similar result is known for
the BKP hierarchy with respect to Schur's Q-function expansion under a similar
condition. In this paper we generalize this result to the case of $\tau(0)=0$.
