  The N component scalar tricritical theory is considered in a non-perturbative
setting. We derive non-perturbative beta functions for the relevant couplings
in $d\leq 3$. The beta functions are obtained through the use of an exact
evolution equation for the so called effective average action. In d=3 it is
established the existence of an ultraviolet stable fixed point for N>4. This
confirms earlier results obtained using the 1/N expansion where such a fixed
point is believed to exist at least for $N\gtrsim 1000$.
