An　new　orthogonal　decomposition　method　and　implementation　algorithm　for　speech　signals　is　proposed　in　this　paper.　From　the　reproducing　kernel　function　of　Hilbert　space　W21[a,　b],　a　set　of　normalized　orthogonal　functions　{φ*j(x)}1n　are　generated.　Based　on　{phi;*j(x)}1n,　speech　signals　can　be　orthogonally　decomposed,　and　the　orthogonal　decomposition　coefficients　can　be　computed　by　a　fast　algorithm　based　on　the　properties　of　reproducing　kernel　function.　This　method　transforms　the　discrete　problem　to　continuous　function　space　and　convert　the　inner　product　computation　problem　in　Hilbert　space　into　function　evaluation　problem　in　some　discrete　points.　The　experiment　results　indicate　that　it　can　be　applied　to　the　reconstruction　and　feature　extraction　of　speech　signals.