  Field equations for n-frames h_a{}^\mu that are possible in the theory of
absolute parallelism (AP) are considered. The methods of compatibility (or
formal integrability) theory enable us to find the non-Lagrangian equation
having unusual kind of compatibility conditions, guaranteed by two (not one)
identities. This 'unique equation' was not noted explicitly in the
classification by Einstein and Mayer of compatible second order equations of
AP.
  It is shown that some equations of AP (including 'unique equation') can be
written in a trilinear form that contains only the matrix of frame density (of
some weight) H_a{}^\mu and its derivatives and not inverse (coframe density)
matrix. The equations are still regular and involutive for degenerate but
finite matrices H_a{}^\mu if rank H_a{}^\mu > 1.
