  The Sun is moving through a warm ($\sim$6500 K) and partly ionized local
interstellar cloud (LIC) with a velocity of $\sim$26 km/s. Recent measurements
of the ionization of the LIC (Wolff et al., 1999) suggest that interstellar
helium in the vicinity of the Sun is 30-40 % ionized, while interstellar
hydrogen is less ionized. Consequently, interstellar helium ions contribute up
to 50% of the total dynamic pressure of the ionized interstellar component. Up
to now interstellar helium ions have been ignored in existing models of the
heliospheric interface. In this paper we present results of a new model of the
solar wind interaction with the interstellar medium, which takes into account
interstellar helium ions. Using results of this model we find that the
heliopause, termination and bow shocks are closer to the Sun when compared to
the model results that ignore $He$ ions. The influence of interstellar helium
ions is partially compensated by solar wind alpha particles, which are taken
into account in our new model as well. Finally, we apply our new model to place
constraints on the plausible location of the termination shock.
