Given an approximate solutionxn of a linear operator equation obtained by a collocation method, an improved solutionx*n+m is obtained fromxn by an «extended collocation method» which consists in solving a further (m)-order linear system instead of an (n+m)-order one, diminishing the effects of rounding error in carrying out the calculations. For a suitable choice of the knot, the method may be recursively performed both by spline approximation and by algebraic and trigonometric polynomial approximation. A numerical example with a two point boundary value problem confirms the advantages of the extended method with respect to the direct one.