In this paper we present a new technique for on-line checking of FPGA-based sequential devices defined by their algorithmic state machines (ASMs). The technique utilizes specific properties of ASMs for achieving the totally self-checking goal with a low hardware overhead. This technique is based on the architecture that consists of two portions: a self-checking sequential device and a separate totally self-checking (TSC) checker. Each of these portions is implemented as a combination of an "evolution" block and an "execution" block. Comparison of code vectors transferred between these blocks provides for the totally self-checking property. The proposed technique does not require any redundant encoding of output words and uses a one-rail design, thereby drastically decreasing the required overhead. The paper presents overhead estimations and results for benchmarks for the proposed architecture.