we consider the problem of sequential change-point detection where 
both the change-points and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory,  we derive a variant of the Bayesian Online Change Point Detector proposed by \cite{fearnhead2007line}
which is easier to analyze than the original version while keeping its powerful message-passing algorithm. 
We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and real-world data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy.