The dynamics of layer formation by salt fingers from the uniform temperature and salinity gradients is studied by direct numerical simulations of the two-dimensional Navier–Stokes equations. It is shown that formation of steps in the model is caused by the parametric variation of the flux ratio ($\gamma\,{=}\,{\overline{wT}}/{\overline{wS}}$) as a function of the density ratio ($R$), which leads to an instability of equilibrium with uniform stratification. These unstable large-scale perturbations continuously grow in time until well-defined layers are formed. Subsequent evolution of the numerical staircases is explained by considering the secondary instabilities of a series of salt finger interfaces.