A method for efficiently determining the path maximum transmission unit (MTU) during a handshake between a source host and a target host across a computer network. During the handshake, each router receives the SYN (synchronization) packet transmitted from the source host, and each router updates the value of the path MTU within the SYN packet when the path MTU value is greater than the MTU of the router. When the SYN packet reaches the target host, the target host also updates the value of the path MTU if the value of the path MTU within the SYN packet is greater than that of the target host. With this sequential checking and updating of the path MTU against their MTUs, the combination of the routers en-route and the target host ensures that the final path MTU is equal to or smaller than the smallest MTU of the various components/networks along the path.