This research guaranteed orthogonal symmetry demonstration to any system function,ensured the formula of demonstration to system function variance.They are the kernel and foundation stone of statistical analysis of global symmetry.By studying how these symmetry functions work in the whole system function,the symmetry of system function can be understood better.As illustrated by the examples,it showed the symmetry of system function clearly by using the Monte-Carlo calculated value of contribution rate as the global sensitivity index of symmetry function.