  A correlation function of two particles with small relative velocities obeys
a sum rule - the momentum integral of the function is determined due to the
completeness of quantum states of the particles. The original sum rule derived
in 1995 suffered from a serious problem: the momentum integral was ultraviolet
divergent in physically interesting cases. We resolve the problem by
considering the sum rule not of a single correlation function but of a sum or
difference of two appropriately chosen correlation functions. The improved sum
rule is shown to work well for the exact Coulomb correlation functions. We
argue that the sum rule can be used to test an accuracy and range of
applicability of correlation functions computed in approximate models. The
neutron-proton correlation function is discussed as an example.
