We calculate with the variational technique the fine structure of a bi
exciton in wurtzite crystals with the effective electron-hole exchange
interaction taken into account. The values of the electron-hole excha
nge integrals are taken from the free exciton GAMMA5-GAMMA6 splitting.
We calculate the biexciton dissociation energy and the ratio of mixin
g of the symmetric and antisymmetric envelopes which arises from the e
lectron-hole exchange interaction. Results are presented for CdS, CdSe
and ZnS crystals.