Using the renormalization group approach proposed by Millis for the itinerant electron systems we calculated the specific heat coefficient γ(T ) for the magnetic fluctuations with susceptibility χ −1 ∼ |δ + ω| α + f (q) near the Lifshitz point. The constant value obtained for α = 4/5 and the logarithmic temperature dependence, specific for the non-Fermi behavior, have been obtained in agreement with the experimental data.