  The problem of time reparameterization is addressed at both the classical and
quantum levels in a Bianchi-I universe in which the matter source is a massive
Dirac spinor field. We take the scale factors of the metric as the intrinsic
time and their conjugate momenta as the extrinsic time. A scalar character of
the spinor field is identified as a representation of the extrinsic time. The
construction of the field equations and quantization of the model is achieved
by solving the Hamiltonian constraint after time identification has been dealt
with. This procedure leads to a true Hamiltonian whose exact solutions for the
above choices of time are presented
