The unconditionally positive-convergent implicit scheme for two-equation turbulence models, originally developed by Mor-Yossef and Levy, is revisited. A compact, simple, and uniform reformulation of the method for the use of both structured and unstructured grid based flow solvers is presented. An analytical proof of the scheme revision is given showing that positivity of the turbulence model solutions and convergence of the turbulence model equations are guaranteed for any time step. Numerical experiments are conducted, simulating two test cases of three-dimensional complex flow fields using structured and hybrid unstructured grids. To demonstrate the overall scheme’s robustness, it is applied to non-linear k- ω and non-linear k- ϵ turbulence models. Results from the numerical simulations show that the scheme exhibits very good convergence characteristics, is robust, and it always preserves the positivity of the turbulence model dependent variables, even for an infinite time step.