A new version of the adiabatic hyperspherical approach (AHSA) is sugge
sted which has significant advantages for the calculation of three-bod
y states with total angular momentum J > 0. The binding energies of al
l bound states of mesic molecules with normal parity are calculated by
the suggested method. Comparison with results of variational calculat
ions and the fast convergence of the method confirm its high efficienc
y.