  The variational methods implemented on a quadratic Yang-Mills type Lagrangian
yield two sets of equations interpreted as the field equations and the
energy-momentum tensor for the gravitational field. A covariant condition is
imposed on the energy-momentum tensor to represent the radiation field. A
generalized pp-wave metric is found to simultaneously satisfy both the field
equations and the radiation condition. The result is compared with that of
Lichn\'{e}rowicz.
