  We demonstrate that a measurement of the impact parameter in one-prong tau
decay can be useful for the determination of the Higgs boson parity in the H/A
--> tau tau; tau --> rho nu decay chain. We have estimated that for a detection
set-up such as TESLA, use of the information from the tau impact parameter can
improve the significance of the measurement of the parity of the Standard Model
120 GeV Higgs boson to 4.5 sigma, and in general by factor of about 1.5 with
respect to the method where this information is not used.
  We also show that the variation in the assumption on the precision of the
measurement of the impact parameter and/or pi's momenta does not affect the
sensitivity of the method. This is because the method remains limited by the
type of twofold ambiguity in reconstructing the tau momentum.
