Abstract: Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)^T=(-<A²q, q>, <A²p, p>)^T=f(q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R^2N, Adp∧dq, H=H₁) with the Hamiltonian
H₁=-<A³q,p>-(1/2)<A²p,p><A²q,q>.
while the nonlinearization of the time part leads to its N-involutive system {H_m}. The involutive solution of the compatible fsystem (H₁), (H_m) is mapped by into the solution of the higher order Kaup-Newell equation.