Kennaugh's pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In this paper, by means of real representation, we first present a necessary and sufficient condition for the general Kennaugh's pseudo-eigenvalue equation having a solution, characterize the explicit form of the solution, and then study the solution of Kennaugh's pseudo-eigenvalue equation. At last, we propose a new technique for finding the coneigenvalues and coneigenvectors of a complex matrix under appropriate conditions in radar polarimetry.