We give a refinement of the linear independence criterion over function fields developed by Anderson, Brownavvell and Papanikolas [Greg W. Anderson, W. Dale Brownavvell, Matthew A. Papanikolas, Determination of the algebraic relations among special F-values in positive characteristic, Ann. of Math. 160 (2004) 237-313]. As a consequence, a function field analogue of the Siegel-Shidlovskii theorem is derived. (C) 2008 Elsevier Inc. All rights reserved.