  We discuss what predictions can be made for one-loop superamplitudes in
maximally supersymmetric Yang-Mills theory by using anomalous dual conformal
symmetry. We show that the anomaly coefficient is a specific combination of
two-mass hard and one-mass supercoefficients which appears in the
supersymmetric on-shell recursion relations and equals the corresponding
tree-level superamplitude. We discuss further novel relations among
supercoefficients imposed by the remaining non-anomalous part of the symmetry.
In particular, we find that all one-loop supercoefficients, except the
four-mass box coefficients, can be expressed as linear combinations of
three-mass box coefficients and a particular symmetric combination of two-mass
hard coefficients. We check that our equations are explicitly satisfied in the
case of one-loop n-point MHV and NMHV amplitudes. As a bonus, we prove the
covariance of the NMHV superamplitudes at an arbitrary number of points,
extending previous results at n <= 9.
