A line search method that uses directions of negative curvature for the optimization of ground and excited multiconfigurational self-consistent field (MCSCF) wavefunctions is suggested. The method is applicable to general MCSCF wavefunctions and not restricted to specific classes of model spaces, such as CASSCF functions. It is shown that the approach can be implemented with Newton or quasi-Newton methods for determination of descent directions. Thus, the method is particularly promising for cases in which it is inconvenient or costly to calculate exact curvature matrices. We demonstrate the viability of the approach by numerical example on the difficult BeO problem.