We propose a set of scanning tunneling microscopy experiments in which the
surface of a superconductor is scanned by a superconducting tip. Potential
capabilities of such experimental setup are discussed. Most important antic
ipated results of such an experiment include the position-resolved measurem
ent of the superconducting order parameter and the possibility to determine
the nature of the secondary component of the order parameter at the surfac
e. The theoretical description based on the tunneling Hamiltonian formalism
is presented.