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Abstract: LHCb is one of the four main experiments of the Large Hadron Collider (LHC) project, which will start at CERN in 2008. The experiment is primarily dedicated to B-Physics and hence requires precise vertex reconstruction. The silicon vertex locator (VELO) has a single hit precision of better than and is used both off-line and in the trigger. These requirements place strict constraints on its alignment. Additional challenges for the alignment arise from the detector being retracted between each fill of the LHC and from its unique circular disc strip geometry. This paper describes the track-based software alignment procedure developed for the VELO. The procedure is primarily based on a non-iterative method using a matrix inversion technique. The procedure is demonstrated with simulated events to be fast, robust and to achieve a suitable alignment precision. [Copyright &y& Elsevier]