The sigma-model in (3 + 1)-dimensions extended by addition of the quartic and sextic terms is investigated. In the presence of a symmetry-breaking potential the existence of both instanton and sphaleron configurations is shown. In order to obtain an explicit sphaleron solution, the sextic and potential terms are retained and the stability problem is studied. On the basis of general arguments the existence of a negative eigenvalue is proven and with some approximation calculated.