A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational positions. Contrary to the standard implicit method by Fincham [Mol. Simul., 8, 165 (1992)], the revised angular momentum approach presented corresponds completely to the leapfrog idea on interpolation of dynamical variables without using any extrapolations. The proposed scheme intrinsically preserves rigid molecular structures and considerably improves stability properties and energy conservation. As is demonstrated on the basis of simulations for water, it allows to reproduce correct results with extra large step sizes of order 5 fs and 10 fs in the cases of energy- and temperature-conserving dynamics, respectively. We show also that iterative solutions can be avoided within our implicit scheme shifting from quaternions to the entire rotation-matrix representation.