The authors propose a modification of the SQP-approach for solving nonlinear programming problems. It is well-known that in the classical approach developed by Wilson, Han and Powell the quadratic subproblems can be infeasible. To overcome this drawback such QP-subproblems are defined, in which the right-hand vector of the constraints ensures feasibility and furthermore, the search direction obtained from this subproblem is a descent direction for a distance function to measure the nonfeasibility of the actual iteration point. After the discussion of the modified quadratic subproblem special attention is given to the update of the penalty parameter in the merit function which is used in the line search phase for the determination of the step length. Under suitable assumptions it is proved that an SQP-method based on these subproblems will be global convergent to a stationary point, i.e. a point which is either a Kuhn-Tucker point, a Fritz-John point of the nonlinear problem, or a stationary point of the above remarked distance function. At the end of the paper the authors give some useful hints for implementation and two illustrative examples.