Versatile gait patterns are observed in quadrupeds according to the locomotion speed, environmental conditions, and animal species. These gait patterns are generated via inter- and intra-limb coordination mechanisms, both of which are controlled in part by an intraspinal neural network called the central pattern generator (CPG). Previous CPG-based models mainly focused on the inter-limb coordination mechanisms and not on the intra-limb coordination mechanisms, although both of them should play a pivotal role in generating various gait patterns. In this study, we present an autonomous decentralized control scheme for quadruped locomotion wherein inter- and intra-limb coordination mechanisms are well coupled. Simulation results show that the quadruped exhibits transitioning between walking and running and the ability to adapt to changes in body properties by appropriately modifying the phase relationship among body points through well-balanced coupling of the inter- and intra-limb coordination mechanisms. We also present a physical robot that we are currently developing.