  The condensate fraction of a homogeneous and dilute Bose gas is expanded as a
power series of $\sqrt{n a^3}$ as $N_0/N = 1 -c_1 (n a^3)^{1/2} -c_2 (n a^3) -
c_3 (n a^3)^{3/2}\hdots.$ The coefficient $c_1$ is well-known as $8/3
\sqrt{\pi}$, but the others are unknown yet. Considering two-body contact
interactions and applying a canonical transformation method twice we developed
the method to obtain the higher order coefficients analytically. An iteration
method is applied to make up a cutoff in a fluctuation term. The coefficients
ares $c_2=2(\pi - 8/3)$ and $c_3=(4/\sqrt{\pi}) (\pi -8/3)(10/3-\pi)$.
