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 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 (162, 171) of said communication network, said plurality of wireless access points (162, 171) comprising at least the first and second wireless access points (162, 171), an evaluation of the best candidate before selection 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 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 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 (162, 171) of said communication network, said plurality of wireless access points (162, 171) comprising at least the first and second wireless access points (162, 171), an evaluation of the best candidate before selection 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 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 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.