A new method for investigating muonium-to-antimuonium conversion is pr
oposed and implemented. The method is based on detecting high-energy e
lectrons from the decay of the muon of antimuonim by a wide-aperture m
agnetic beta spectrometer. The importance of exploring muonium-to-anti
muonium conversion is theoretically substantiated. The setup for the p
roposed experiment to study the conversion process is described, and p
rocedures for analysis of resulting data and of background conditions
at this setup are discussed. With the aid of the proposed method, the
probability of muonium-to-antimuonium conversion is investigated exper
imentally in a surface-muon beam from the phasotron installed at JINR.
New experimental upper limits are obtained for the probability of the
conversion process (W(<M(M)over bar>)) and for the weak-interaction c
onstant in this process (G(<M(M)over bar>)): W(<M(M)over bar>)less tha
n or equal to 47X10(-7) and G(<M(M)over bar>)less than or equal to 0.1
4G(F) (at a 90% C.L.). The mass of the doubly charged Higgs boson H++,
which is responsible for the conversion process M-->(M) over bar, is
found to be bounded from below as M(++)greater than or equal to 210 Ge
V/c(2).