A scheme for dealing with the quantum three-body problem is presented to separate the rotational degrees of freedom completely from the internal ones. In this method, the three-body Schridinger equation is reduced to a system of coupled partial differential equations, depending only upon three internal variables. For arbitrary total orbital angular momentum l and the parity (-1)l+λ (λ=0 or 1), the number of the equations in this system is l+1-λ. By expanding the wavefunction with respect to a complete set of orthonormal basis functions, the system of equations is further reduced to a system of linear algebraic equations.