This　paper　proposes　a　novel　high-order　associative　memory　system　(AMS)　based　on　the　discrete　Taylor　series　(DTS).　The　mathematical　foundation　for　the　new　AMS　scheme　is　derived,　three　training　algorithms　are　proposed,　and　the　convergence　of　learning　is　proved.　The　DTS-AMS　thus　developed　is　capable　of　implementing　error-free　approximation　to　multivariable　polynomial　functions　of　arbitrary　order.　Compared　with　cerebellar　model　articulation　controllers　and　radial　basis　function　neural　networks,　it　provides　higher　learning　precision　and　less　memory　request.　Furthermore,　it　offers　less　training　computation　and　faster　convergence　rate　than　that　attainable　by　multilayer　perceptron.　Numerical　simulations　show　that　the　proposed　DTS-AMS　is　effective　in　higher　order　function　approximation　and　has　potential　in　practical　applications.