  We consider N=1 SUSY gauge theory in six dimensions in components and show
that provided the Dynkin indices of the matter fields representations satisfy
the relation $\sum T(R)= C_2(G)$, the gauge sector is completely one-loop
finite. In the matter sector the UV divergences form several invariant
structures some of which are cancelled in physical amplitudes. Thus, the theory
which is in general non-renormalizable may be consistent and even finite.
Consequences for the SUSY GUT models in the bulk are briefly discussed.
