The invention relates to a method consisting of connecting each fax machine (14, 14 '') to a network of direct transmission (100) and a network of indirect economic transmission (101) and transmission respectively fax from one machine to another (20) and a warning (21) to transmit the fax through network indirect transmission (101) and through the direct transmission network (100). Each fax machine (14, 14 ') comprises a transmitter block for issuing warnings for fax transmission and notified faxes, connected to a network direct transmission (100) and a network of indirect transmission (101).
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