The article introduces a new transformation procedure into an analytic construction of a Reissner-Mindlin model for curved comosite laminates, layers of which possess monoclinic symmetry. To avoid unnecessary complexities of the mathematical description, teh original three-dimensional elasticity problem is first formulated in an intrinsic form. Then, the variational-asymptotic method is used to perform a rigorously dimensional reduction to split the nonliner three-dimensional problem into a nonlinear two-dimensional surface analysis and a linear one-dimensional through-the-thickness analysis. This takes advantage of two small geometric parameters inherent in the structure. However, it is not easy to relate the derived energy functional with a simple and practical engineering model, such as the Reissner-Mindlin model. To obtain the energy functional that is of practical use, we proceed a little different manner unlike the previous works. By solving a system of linear algebraic equations composed of modified equilibrium and compatibility equations, an hybrid energy transformation procedure is systematically performed to eliminate all patial derivatives of the two-dimensional shell variable with respect to in-plane coordinates. Then, the two-dimensional generalized and transverse shear stiffness matrices for the Reissner-Mindlin model are efficiently calculated without relaxing the established warping constraints and performing several approximation procedures introduced into the previous works.