In this paper, we propose an on-board diagnosis method for the embedded system based on the model-based diagnosis. We introduce the qualitative model for the embedded system by transforming the continuous dynamics of components into the discrete state transition system which is represented in the circuit called a synchronous Boolean tree (SBT). The SBT is a network of the (temporal) propositional operations with latches. The faults of components are reduced to the stuck-at faults in SBT. We present a many-value tableau method for the SBT diagnosis, which allows the efficient search for the faulty parts by propagating the observed anomaly through the SBT.