We are concerned with the solution of the bound constrained minimization problem {minf(x), l≤x≤u}. For the solution of this problem we propose an active set method that combines ideas from projected and nonmonotone Newton-type methods. It is based on an iteration of the form x <Superscript> k+1</Superscript>=[x <Superscript> k </Superscript>+α...</superscript></superscript>