  When the number of particles $N$ is finite, the noncolliding Brownian motion
(BM) and the noncolliding squared Bessel process with index $\nu > -1$
(BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial
configurations. In the present paper we prove that, if initial configurations
are distributed with orthogonal symmetry, they are Pfaffian processes in the
sense that any multitime correlation functions are expressed by Pfaffians. The
$2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians
processes are explicitly obtained by the equivalence between the noncolliding
BM and an appropriate dilatation of a time reversal of the temporally
inhomogeneous version of noncolliding BM with finite duration in which all
particles start from the origin, $N \delta_0$, and by the equivalence between
the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared
generalized meander starting from $N \delta_0$.
