Any coadjoint orbit of the general linear group can be canonically parameterized using an iteration method, where at each step we turn from the matrix of a transformation A to the matrix of the transformation that is the projection of A parallel to an eigenspace of this transformation to a coordinate subspace. We present a modification of the method applicable to the groups SONℂ and SpNℂ. One step of the iteration consists of two actions, namely, the projection parallel to a subspace of an eigenspace and the simultaneous restriction to a subspace containing a co-eigenspace. The iteration gives a set of couples of functions p_k, q_k on the orbit such that the symplectic form of the orbit is equal to (Formula Presented.). No restrictions on the Jordan form of the matrices forming the orbit are imposed. A coordinate set of functions is selected in the important case of the absence of nontrivial Jordan blocks corresponding to the zero eigenvalue, which is the case dim ker A = dim ker A². It contains the case of general position, the general diagonalizable case, and many others.