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In applications, the signals used for order tracking of rotating machinery are often distorted by non-order components, such as the fixed frequencies arising from power-frequency interferences, and local structure resonances, which may render the results from the analysis meaningless or inaccurate. Independent component analysis (ICA), as a statistical method, has the ability to segregate multiple-sources signals into independent signals. In this paper, a scheme to reduce the non-order noise for order tracking analysis in computer order tracking (COT) based on ICA is presented, in which FastICA scheme is exploited to separate observed (mixed) signals into the order components and the non-order noise in the angular domain. The ambiguities of ICA are also solved in the scheme, which make it feasible to condition monitoring and fault diagnosis applications of rotating machinery. The approach is applied to simulation experiments. Analysis results give positive support to the presented approach.