The chemical equation for H2 formation (in non-equilibrium condition) and the energy equation were solved numerically like a two boundary value problem. The values of the chemical parameter x, the gas temperature T and the mass density ρ, were obtained explicitly as functions of time and they were compared with the change in the mean density produced by the free-fall. The ability of H2 formation to act as a direct non-linear amplifier of density inhomogeneities in prestellar clouds depends critically on the initial values of the number density of particles n0, the temperature T0 and the percentage of chemical heat input to the gas, ∊. In particular, if the remainder of the binding energy of H2 formation is radiated by the grains, H2 formation can induce fragmentation in a contracting cloud providing that T0 > 60 K and n0 ≳ 102 cm−3.