  We compute the three-loop anomalous dimension of the BMN operators with
charges J=0 (the Konishi multiplet) and J=1 in N=4 super-Yang-Mills theory. We
employ a method which effectively reduces the calculation to two loops. Instead
of using the superconformal primary states, we consider the ratio of the
two-point functions of suitable descendants of the corresponding multiplets.
  Our results unambiguously select the form of the N=4 SYM dilatation operator
which is compatible with BMN scaling. Thus, we provide evidence for BMN scaling
at three loops.
