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The problem of diagnosability of a system with three-valued test outcomes was considered in earlier works -. However all these works assume the system to be modeled as in . In this correspondence, we consider a more general model of the system and study the diagnosability criteria in presence of three-valued test outcomes. In this model, each unit is tested jointly by a number of other units of the system as opposed to each test being carried out by a single unit of the system as in . Necessary and sufficient conditions for the diagnosability of a system under this general model have been presented in this correspondence. Throughout the correspondence, diagnosability without repair has been considered.