This paper presents a new method for solving the basic problem in the “modeltrust region” approach to large scale minimization: Compute a vector x such that 1/2xTHx + cTx = min, subject to the constraint ‖x‖2≤a. The method is a combination of the CG method and a projection and contraction (PC) method.The first (CG) method with x0 = 0 as the start point either directly offers a solution of the problem, or--as soon as the norm of the iterate greater than a, --it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.