In this paper a new measure in system-level diagnosis for hypercube multicomputer systems is defined. One-step diagnosis of hypercubes which involves only one testing phase during which processors test each other is discussed. Two different kinds of one-step diagnosis are considered: one called one-step diagnosis and studied earlier by other researchers and the other called onestep diagnosis with the forbidden faulty sets (one-step-FFS) and studied first here in the context of application to hypercubes. One of the two main results presented here is a proof that the degree of diagnosability of the (n)-dimensional hypercube (for short, (n)-cube), where (n \geq 4), increases from (n) to (2 n-2) as the diagnosis strategy changes from the one-step strategy to the one-step-FFS strategy. The other main result is the proof that if the fault bound; i.e., the upper bound on the possible number of faulty processors, is kept to the same number (\boldsymbol{n}) in both cases of one-step and one-step-FFS diagnosis, then the one-step-FFS strategy requires ([n / 2]+1) testing links per processor, whereas the one-step strategy requires (n) testing links per processor. An algorithm for selecting ( (\mid n / 2]+) 1) (n / 2) (2-way) links in an (n)-cube for use as testing links is presented. 1993 Academic Press, Inc.