A source of a Distributed Denial-of-Service (DDoS) attacks are one of the major threats to the Internet today. DDoS attacks can be recognized by the traffic they make using the IP traceback technique [5]. In general, there are only a limited number of routers and the computers involved in an attack session are noticed. Therefore, only marking those involved nodes for traceback purpose is needed, rather than marking each node of the Internet, as the existing schemes does. Based on this finding, a novel Marking on Demand (MOD) scheme based on the DDPM mechanism to dynamicaly distribute marking IDs in both temporal and space dimensions is available. The available MOD scheme can traceback to all probable sources of DDoS attacks, which is not feasible for the existing DDPM schemes. However, the existing MOD framework needs to be extended since it suffers from both false positive and false negative rate. This paper aims to extend the existing MOD scheme by using a 32-bit marking field in order to reduce the shortcomings and to avoid the problem caused by packet fragmentation due to increase in marking length.