Let Γ be a d-summable surface in Rm, i.e., the boundary of a Jordan domain in Rm, such that ∫01NΓ(τ)τd-1dτ<+∞, where NΓ(τ) is the number of balls of radius τ needed to cover Γ and m-1dm, the operator SΓ∗ transforms functions of the higher order Lipschitz class Lip(Γ,k+α) into functions of the class Lip(Γ,k+β), for β=mα-dm-d. In addition, an estimate for its norm is obtained.