This paper introduces a novel blind on-line dereverberation algorithm for speech signals based on a natural gradient deconvolution algorithm. Existing blind dereverberation algorithms often employ a structure that performs speech prewhitening using LPC analysis followed by a blind deconvolution step applied to the LPC residual. Here it is shown that better performance can be achieved by respecting the correct ordering of the stationary (room response) and nonstationary filters (LPC filters) within the dereverberation algorithm. Furthermore this makes replicating the dereverberation filter unnecessary.