  We consider, in the harmonic superspace approach, the six-dimensional N=(1,0)
supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet.
The superficial degree of divergence is evaluated and the structure of possible
one-loop divergences is analyzed. Using the superfield proper-time and
background-field technique, we compute the divergent part of the one-loop
effective action depending on both the gauge multiplet and the hypermultiplet.
The corresponding counterterms contain the purely gauge multiplet contribution
together with the mixed contributions of the gauge multiplet and
hypermultiplet. We show that the theory is on-shell one-loop finite in the
gauge multiplet sector in agreement with the results of [1]. The divergences in
the mixed sector cannot be eliminated by any field redefinition, implying the
theory to be UV divergent at one loop.
