Method of safeguarding anonymity during a telephone communication and telecommunication system for implementing the method

Method of safeguarding anonymity during a communication to a destination (202, 209), between a caller (201) and a called user (202), the communication exhibiting an anonymous character, the method is characterized in that it comprises the following steps: - on receipt of a response from the destination (202, 209) to the communication sent by the caller (201), placing of the caller (201) on standby, - analysis of the response received from the destination (202, 209), so as to determine whether the destination (202, 209) corresponds to the voice messaging (209) of the called user (202), - in case of positive determination, broadcasting to the caller (201) of an anonymous greeting message (207) in which the identity of the called user (202) is masked.