We explicitly constructed the generators of SU(n+1) group which commute
with the supercharges of N=4 supersymmetric CP(n) mechanics in the
background U(n) gauge fields. The main feature of our construction is that
the corresponding Hamiltonian can be represented as a direct sum of two
Casimir operators: one Casimir operator on SU(n+1) group contains our
bosonic and fermionic coordinates and momenta, while the second one, on
the SU(1,n) group, is constructed from isospin degrees of freedom only.