We recently demonstrated noninvasive detection of fetal aneuploidy by shotgun sequencing cell-free DNA in maternal plasma using next-generation high throughput sequencer. However, GC bias introduced by the sequencer placed a practical limit on the sensitivity of aneuploidy detection. In this study, we describe a method to computationally remove GC bias in short read sequencing data by applying weight to each sequenced read based on local genomic GC content. We show that sensitivity is limited only by counting statistics and that sensitivity can be increased to arbitrary precision in sample containing arbitrarily small fraction of fetal DNA simply by sequencing more DNA molecules. High throughput shotgun sequencing of maternal plasma DNA should therefore enable noninvasive diagnosis of any type of fetal aneuploidy.