In this paper, the derivation of the Bayesian Bhattacharyya bound for discrete-time filtering as proposed ina paper by Reece and Nicholson is revisited. It turns out that the results presented in the aforementioned contribution are incorrect, as some expectations appearing in the information matrix recursions are missing. This paper gives a generalized derivation of the N-th order Bayesian Bhattacharyya bound and presents corrected expressions for the case N = 2. A nonlinear toy example is used to illustrate the results