  A canonical quantization scheme applied to a classical supersymmetric system
with quadratic in momentum supercharges gives rise to a quantum anomaly problem
described by a specific term to be quadratic in Planck constant. We reveal a
close relationship between the anomaly and the Schwarzian derivative, and
specify a quantization prescription which generates the anomaly-free
supersymmetric quantum system with second order supercharges. We also discuss
the phenomenon of a coupling-constant metarmorphosis that associates quantum
systems with first-order supersymmetry to the systems with the second-order
supercharges.
