Abstract：In this note, a detective matrix-based  distributed algorithm is proposed to address a distributed minimum-time  consensus prediction problem for discrete-time high-order multi-agent systems (MASs). Therein, each agent   predicts  the consensus value merely using the minimum length of  individual  and/or neighboring successive     position time    series. Compared to most existing algorithms that  could only predict constant consensus values for first-order linear MASs, the present method could predict  consensus manifolds for high-order linear MASs  as well, which could be time-varying.  Finally, both the effectiveness and superiority of the proposed distributed minimum-time consensus algorithm are substantiated by numerical simulations.