  A relaxation method is employed to study a rotating dense Bose-Einstein
condensate beyond Thomas-Fermi approximation. We use a slave-boson model to
describe the strongly interacting condensate and derive a generalized
non-linear Schr\"odinger equation with kinetic term for the rotating
condensate. In comparison with previous calculations, based on Thomas-Fermi
approximation, significant improvements are found in regions, where the
condensate in a trap potential is not smooth. The critical angular velocity of
the vortex formation is higher than in the Thomas-Fermi prediction.
