Parabolic equations with convection, diffusion and reaction terms are used to model many physical and biological systems. In many applications the unknowns represent quantities that cannot be negative such as concentrations of chemical compounds or population sizes. Widely used schemes such as Euler or Runge-Kutta may produce negative solutions because of truncation errors and may then become unstable. We propose a new scheme that guarantees the positivity of the solutions for arbitrary step sizes. We give some examples.