The article deals with the well known Rückert-Lefschetz scheme of investigation of implicit functions that are defined with finite systems f(x) = 0 of equations with analytical left hand sides. It is proved that this scheme is not effective. This means that this scheme does not allow to define jets of implicit functions using only jets of left hand sides of equations under considerations even for structurally stable systems of equations (although it allows to describe the possible structure of the set of implicit functions). There is presented some modification of the Rückert-Lefschetz scheme which, in basic cases, allows to define jets of implicit functions using only jets of left hand sides of equations under considerations even for structurally stable systems of equations.