Core-stateless mechanisms achieve better scalability by reducing the complexity of fair queuing, which usually needs to maintain states, manage buffers, and perform flow scheduling on a per flow basis. However, they require per-packet relabeling in the core routers. We propose a core-stateless fair bandwidth allocation scheme without maintaining per flow state in core routers. Furthermore, it does not need relabeling, which is commonly used in existing core-stateless schemes. Packets are labeled only once in the entrance of the network according to the characteristics of the flow to which the packets belong. No matter TCP or UDP flows can get their fair share rate by the proposed scheme. Moreover, the scheme employs an estimation of number of active flows in the core routers. The estimation can be used to provide fair share rate without maintaining per flow states. The packets belonging to the flows whose rates exceed the estimated fair share rate are dropped. The novel scheme is called core-stateless labeling fairness (CSLF). We present and discuss simulations on the performance under different traffic scenarios.