For a multi-extrema search method to be systematic, there are three main difficulties : (a) attraction of the previously found point; Lpar;b) definiteness of the search trajectory between two points ; (c) exhaustiveness of the overall search. In this paper it is shown that these difficulties can be overcome in the following ways : (a) destabilization of the previously found point by transforming it into a saddle point ; (b) force the search trejectory to remain on the invariant analytical line between two points, and (c) stabilization-destabilization alternation of all points found.