  We study the parity effect of the particle number in the interference fringes
of a Bose-Einstein condensate released from a double-well potential. For a
coherently splitting condensate in the double-well potential, with a decoupled
two-mode Bose-Hubbard model, there is well-known phase diffusion because of
interatomic interactions. After a specific holding time of the double-well
potential, the phase diffusion will make the interference patterns in the
density distribution depend strongly on the parity of the total particle number
by further overlapping two condensates. This parity effect originates from the
quantized relative phase about the total particle number. The experimental
scheme to observe this "even-odd" effect of the particle number is discussed.
