The linear double-diffusive stability of a two-dimensional infinite horizontal layer stratified vertically by temperature and solute concentration is analyzed numerically by the Galerkin method for the case of temperature dependent kinematic viscosity and molecular salt diffusivity (aqueous solution of NaCl). The horizontal boundaries are shear-free and perfectly conducting. The results for the direct mode (‘finger regime’) show that, in contrast to the constant properties case, the critical wave-number increases with the solute Rayleigh number and the critical thermal Rayleigh number is reduced from its corresponding constant properties value. Two different branches exist for solute Rayleigh number larger than some fixed value in the case of the oscillatory mode (‘diffusive regime’). The less stable branch is characterized by a high wave-number.