Method for switching the connection of a mobile station , from a first point of wireless access to a communication network of the local area network type comprising a wireless communication coverage extension system to which the mobile station is connected, to a second point of wireless access to said network , the method being implemented in a so-called "connection-management" device of said communication network , the method comprising: - selecting (S2) the second wireless access point as the best candidate for a wireless connection of the mobile station to said network , the second wireless access point being selected from a plurality of wireless access points of said communication network , said plurality of wireless access points comprising at least the first and second wireless access points , an evaluation (S1) of the best candidate before selection (S2) being made in accordance with a predetermined criterion, - seeking the switching of the wireless connection of the mobile station from the first wireless access point to the second wireless access point , in accordance with a protocol message in this regard, and, - if said mobile station does not implement the switching of the connection sought in response to the protocol message sent: ∘ modifying (S3) a value of a transmission parameter of at least the first wireless access point , the modified value of said parameter being of such a nature as to degrade the transmission performances between the first wireless access point and the mobile station compared with a transmission based on the value of said parameter before modification, ∘ transmitting to the mobile station a message comprising a proposal to connect to the second wireless access point . - selecting (S2) the second wireless access point as the best candidate for a wireless connection of the mobile station to said network , the second wireless access point being selected from a plurality of wireless access points of said communication network , said plurality of wireless access points comprising at least the first and second wireless access points , an evaluation (S1) of the best candidate before selection (S2) being made in accordance with a predetermined criterion, - seeking the switching of the wireless connection of the mobile station from the first wireless access point to the second wireless access point , in accordance with a protocol message in this regard, and, - if said mobile station does not implement the switching of the connection sought in response to the protocol message sent: ∘ modifying (S3) a value of a transmission parameter of at least the first wireless access point , the modified value of said parameter being of such a nature as to degrade the transmission performances between the first wireless access point and the mobile station compared with a transmission based on the value of said parameter before modification, ∘ transmitting to the mobile station a message comprising a proposal to connect to the second wireless access point . ∘ modifying (S3) a value of a transmission parameter of at least the first wireless access point , the modified value of said parameter being of such a nature as to degrade the transmission performances between the first wireless access point and the mobile station compared with a transmission based on the value of said parameter before modification, ∘ transmitting to the mobile station a message comprising a proposal to connect to the second wireless access point . <EOS>