This paper describes a new technique to stabilize meshless methods used in conjunction with point-based integration. The method proposed is based on the finite increment calculus (FIC) concepts for convection-dominated problems. In this paper a finite increment gradient operator is defined in such a way that second-order derivatives are included. This operator is then used in the context of a variational formulation of an elliptic problem in order to define a stabilized numerical procedure. For simplicity, the Poisson equation will be used in this paper to illustrate the method, although more general elliptic problems can be equally treated. An eigenvalue analysis will be carried out in order to demonstrate that no mechanisms are present in the resulting equations. Finally, a simple example will illustrate the technique. Copyright © 2000 John Wiley & Sons, Ltd.