This paper is concerned with a specific class of methods for general quadratic programming, called intertia-controlling quadratic programming (ICQP). ICQP methods use a linearly independent subset of constraints, known as a working set, to define a search direction and multiplier estimates. Moreover, in ICQP, constraint deletions are restricted in order to control the inertia of the reduced Hessian matrix, which is never permitted to have more than one nonpositive eigenvalue. \par When solving a QP type problem, at times, there exist points where it is difficult to verify the optimality. Those points are called dead points. In this paper, a computational algorithm is given to determine if a dead point is a local minimizer. \par The authors caution about some problems inherent to their algorithm. No computational example is given in this paper. The algorithm, they warn, could take a ``reasonable amount of computational time'' and could also cycle.