The linear stability of an infinite horizontal double diffusive layer stratified vertically by temperature and solute concentration is analyzed numerically for the case of temperature-dependent viscosity and salt diffusivity. The one-dimensional steady basic state associated with the variable properties is characterized by zero fluid velocity, a linear temperature profile and a non-linear salinity distribution. The horizontal boundaries are shear-free and perfectly conducting. The eigenvalue problem for the linearized perturbation equations is resolved numerically by the Galerkin method. The results for the direct mode (’finger regime’) show that, in contrast to the constant properties case, the critical wavenumber increases with the solute Rayleigh number (Ra-s) and the critical thermal Rayleigh number is reduced from its corresponding constant properties value. The behavior of the oscillatory mode (’diffusive regime’) is more complex, and two different branches exist for Ra-s larger than some fixed value. The least stable branch is characterized by a high wavenumber while the second branch by a small wavenumber.