The particle inconsistency problem significantly influences the calculation accuracy in the smoothed particle hydrodynamics (SPH) method. In the present study, we investigate primarily the influence of the particle inconsistency on the first derivative of field functions and discuss the behavior of several methods of dealing with this problem. In addition, we propose a new approach by which to compensate for this problem, especially for functions having a non-zero second derivative, that is less computational demanding, as compared to the finite particle method (FPM). The performance of the new approach is verified by a series of numerical study in one and two dimensional problems.