Anunstructuredmeshfinitevolumediscretisationmethodforsimulatingdiffusioninanisotropicmediaintwo-dimensionalspaceisdiscussed.Thistechniqueisconsideredasanextensionofthefullyimplicithybridcontrol-volumefinite-elementmethodanditretainsthelocalcontinuityofthefluxatthecontrolvolumefaces.Aleastsquaresfunctionrecon-structiontechniquetogetherwithanewfluxdecompositionstrategyisusedtoobtainanaccuratefluxapproximationatthecontrolvolumeface,ensuringthattheoverallaccuracyofthespatialdiscretisationmaintainssecondorder.Thispaperhighlightsthatthenewtechniquecoincideswiththetraditionalshapefunctiontechniquewhenthecorrectiontermisneglectedandthatitsignificantlyincreasestheaccuracyofthepreviouslinearschemeoncoarsemesheswhenappliedtomediathatexhibitverystrongtoextremeanisotropyratios.Itisconcludedthatthemethodcanbeusedonbothregularandirregularmeshes,andappearsindependentofthemeshquality.