A communication handover method, involving a mobile device that had established with a communication device a communication over IP via an agent device serving as a home agent for said mobile device, a first anchor point and a first radio access device belonging to an Internet protocol communication network with hierarchical mobility management, said mobile device having first temporary local and regional addresses recorded with said first anchor point and with said home agent device, characterized in that it consists, when said mobile device, while moving, detects a second access device connected to a second anchor point of said network, itself connected to said home agent device, of performing the following combination of steps: i) communicating to said mobile device the address prefix of said second access device so that it can create from it second temporary local and regional addresses, ii) communicating said second temporary local and regional addresses to said first anchor point so that it can save that second temporary local address as a match for the second temporary regional address, iii) communicating said second temporary regional address and a home IP address of said mobile device, as well as information data having a value indicating temporary double addressing to said home agent device so that it can save that second temporary regional address as a match for said home IP address, then send the packets intended for said mobile device to the first and second anchor points designated by said first and second temporary regional addresses stored as a match for said home IP address, iv) disconnecting said mobile device from the first access device, then deleting from said home agent device the record of the first temporary regional address of the mobile device as a match for said home IP address, in order to transmit to the latter the packets intended for it, via said home agent device, said second anchor point and said second access device. i) communicating to said mobile device the address prefix of said second access device so that it can create from it second temporary local and regional addresses, ii) communicating said second temporary local and regional addresses to said first anchor point so that it can save that second temporary local address as a match for the second temporary regional address, iii) communicating said second temporary regional address and a home IP address of said mobile device, as well as information data having a value indicating temporary double addressing to said home agent device so that it can save that second temporary regional address as a match for said home IP address, then send the packets intended for said mobile device to the first and second anchor points designated by said first and second temporary regional addresses stored as a match for said home IP address, iv) disconnecting said mobile device from the first access device, then deleting from said home agent device the record of the first temporary regional address of the mobile device as a match for said home IP address, in order to transmit to the latter the packets intended for it, via said home agent device, said second anchor point and said second access device.