Shi-Hui et al. proposed a new public key cryptosystem using ergodic binary matrices. The security of the system is derived from some assumed hard problem based on ergodic matrices over GF(2). In this note, we show that breaking this system, with a security parameter n (public key of length 4n² bits, secret key of length 2n bits and block length of length n² bits), is equivalent to solving a set of n⁴ linear equations over GF(2) which renders this system insecure for practical choices of n.