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

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... r velocity of the vortex formation is higher than in the Thomas-Fermi prediction.