  The field theoretic renormalization group and operator product expansion are
applied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamic
turbulence. The anomalous scaling emerges as a consequence of the existence of
certain composite fields ("operators") with negative dimensions. The anomalous
exponents for the correlation functions of arbitrary order are calculated in
the two-loop approximation (second order of the renormalization-group
expansion), including the anisotropic sectors. The anomalous scaling and the
hierarchy of anisotropic contributions become stronger due to those
second-order contributions.
