Network Functions (NFs) are deployed in networks for a variety of purposes, e.g. monitoring, security, or performance optimization. During packet processing, NF maintains the states of processed packets and/or manipulates packets based on these states. Some of these states are per-flow states while others are multi-flow states. With the emerging of network function virtualization (NFV), it is common to deploy an NF across multiple middleboxes for high processing capability. In this case, per-flow states can be maintained by each middlebox as its local states. The multi-flow states are global states that are shared among middleboxes. We propose a network function framework, Coordinator for Global States (CoGS), to scale a network function with global states across distributed middleboxes. A coordinator is adopted to manage global states for middleboxes. Meanwhile, each middlebox is able to access the states and process packets based on the global states. Our evaluation shows that the CoGS coordinator can handle more than 1 million state operations per second. With CoGS to manage the global states, the distributed NF achieves nearly linear scalability with a dozen of middleboxes.