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The condensate fraction of a homogeneous and dilute Bose gas is expanded as apower 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 contactinteractions and applying a canonical transformation method twice we developedthe method to obtain the higher order coefficients analytically. An iterationmethod is applied to make up a cutoff in a fluctuation term. The coefficientsares $c_2=2(\pi - 8/3)$ and $c_3=(4/\sqrt{\pi}) (\pi -8/3)(10/3-\pi)$.

Higher order terms in the condensate fraction of a homogeneous and dilute Bose gas