  According to [8] if the stationary Schroedinger equation on n-dim. Riemann
space admits R-separation of variables (i.e. separation of variables with a
factor R), then the underlying metric is necessarily isothermic. An important
sub-class of isothermic metrics are the so called binary metrics. In this paper
we study conditions for vanishing of components C_ijkl of Weyl tensor of
arbitrary 4-binary metrics. In particular all 4-binary metrics for which C_ijij
are the only non-vanishing components are classified into four classes.
Finally, conformally flat metrics of the last class are isolated.
