We prove that, under a cfl condition, the explicit upwind finite vol-ume discretization of the convection operator C(u) = ∂ t (ρu) + div(uq), with a given density ρ and momentum q, satisfies a discrete kinetic energy decrease property, provided that the convection operator satis-fies a "consistency-with-the-mass-balance property", which can be simply stated by saying that it vanishes for a constant advected field u.