The　concept　of　quasi　-zero　-stiffness　(QZS)　isolator　was　proposed　in　recent　decades　for　lowfrequency　vibration　isolation.　However,　the　QZS　feature　is　preserved　only　in　the　vicinity　of　the　equilibrium　point,　which　causes　a　dissatisfactory　isolation　effect　especially　when　experiencing　large　excursion.　Therefore,　extending　the　QZS　displacement　range　is　very　crucial　for　improving　the　isolation　performance.　This　paper　proposes　a　magnetic　higher　-order　stable　QZS　mechanism　to　obtain　a　very　wide　QZS　displacement　range.　The　design　criteria　for　the　higher　-order　QZS　property　with　stable　static　equilibrium　point　are　expounded.　The　frequency　response　characteristics　of　the　higher　-order　QZS　isolator　are　analyzed　without　involving　polynomial　approximation.　The　complicated　nonlinear　dynamic　behaviors　are　investigated　in　detail.　The　vibration　isolation　performance　is　compared　with　conventional　QZS　isolator　and　non-QZS　isolator,　revealing　the　advantages　of　the　higher　-order　QZS　isolator.　An　experimental　prototype　of　the　5th　-order　QZS　isolator　is　fabricated　and　tested,　exhibiting　greatly　superior　vibration　isolation　performance　in　comparison　to　the　1st　-order　QZS　isolator　and　non-QZS　isolator.