  We give a local classification of ({\kappa},{\mu},\u{psion}=const.)-contact
metric manifold (M,{\phi},{\xi},{\eta},g) with {\kappa}<1 which satisfies the
condition" the Boeckx invariant function
I_{M}=((1-({\mu}/2))/(\surd(1-{\kappa}))) is constant along the integral curves
of the characteristic vector field {\xi}".
