We investigate a possibility of scale invariant but non-conformal
supersymmetric field theories from a perturbative approach. The explicit
existence of monotonically decreasing a-function that generates beta-functions
as a gradient flow provides a strong obstruction for such a possibility at
two-loop order. We comment on the "discovery" of scale invariant but
non-conformal renormalization group trajectories via a "change of scheme" in
(4-\epsilon) dimension proposed in literatures.