We propose the generalized nonlinear chiral supermultiplet which is defined in terms of 2n bosonic N = 2(n + 1) superfields subjected to the nonlinear constraints. The guiding idea of our construction is its invariance under the action of the SU(n+1) group. With this supermultiplet we were able to find the complete SU(n + 1) invariant simplectic structure and first, linear in the fermionic variables, the terms in the supercharges which anticommute on the Hamiltonian describing the motion of the particle over the CP~n manifold.
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