Non-forking independence in stable theories

We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets, without having to use the full strength of the work of the seminal work of Kim and Pillay. The results in this note (which are surely well-known among most model theorists) essentially use that types over models in a stable theory are stationary.