Finite impulse response (FIR) filters are commonly used in many signal processing systems. In some cases, such as space systems, FIR filters are exposed to radiation sources that cause errors. A number of techniques can be used to protect against those errors. One of them is the use of an arithmetic residue replica of the FIR filter. This replica has a lower cost than the original filter and therefore reduces the overhead compared with replicating the filter. However, some errors may not be detected by the arithmetic residue replica. In this brief, schemes that avoid undetected errors are presented. The proposed techniques are implemented and evaluated showing that they can detect all single errors affecting register bits. The results also show that their implementation requires only a small overhead in circuit complexity for the existing residue-based fault-tolerant FIR filters.