Parametrizing the nucleon-nucleon scattering matrix above the inelastic threshold

All representations presently being used in analyses of nucleon-nucleon scattering above the inelastic threshold are flawed by lack of implicit unitarity, generality, or failure to encode reasonable physical behavior. We examine unitarity from the point of view of an extended $K$ matrix, and derive a representation which is unitary, general, and which uses physically interpretable, bounded parameters.