The evolution of a binary system consisting of a 8M. and 5.5M. star ha
s been studied in the conservative approximation of Case B mass transf
er. Specific attention is given to the effect of exchange between the
orbital angular momentum and the spin angular momentum as the primary
component evolves to a red giant and in the phase of mass transfer. It
has been found that the system considering the spin angular momentum
will evolve to a longer orbital period and with a smaller endmass of t
he primary. It shows that the spin angular momentum cannot be neglecte
d in the calculating of the evolution of binary systems.