Comparison-based diagnosis is a realistic approach to detect faults in multiprocessor systems. The Maeng, Malek (MM) model for comparison-based diagnosis defines a strategy based on sending the same input (or task) from a processor to some pair of distinct neighboring processors, and then comparing their responses. Sengupta and Dahbura proposed a further modification of the MM model, called the model, in which any processor has to test another two processors if is adjacent to them. Sengupta and Dahbura presented a -time diagnosis algorithm for general diagnosable systems under the model, where is the number of processors in the system. By exploiting the cycle decomposition property, we improve the above result by presenting a -time diagnosis algorithm for a class of hypercube-like networks under the model.