Bose has developed a parallel unordered coding scheme using only r checkbits for 2r information bits. This code can detect all unidirectional errors and requires simple parallel encoding/decoding. The information symbols can be separated from the check symbols. However, the information symbols containing all-0's and all-1's need to be transformed to two other information symbols. This allows one to reduce the number of checkbits over Berger code by 1. Since information symbols containing a power-of-two number of bits are quite common, this coding scheme should become quite popular. In this paper, a modular, economical and easily testable totally self-checking (TSC) checker design for the above code is described. The TSC concept is well-known for providing concurrent error detection of transient as well as permanent faults. The design is self-testing with at most only 2r+16 codeword tests. This means that if k is the number of information bits, the size of the codeword test is only O(log2k). This is the first known TSC checker design for this code.