This　work　is　a　continuation　of　our　previous　work　[Z.-Q.　Shao,　D.-X.　Kong,　Y.-C.　Li,　Shock　reflection　for　general　quasilinear　hyperbolic　systems　of　conservation　laws,　Nonlinear　Anal.　TMA　66　(1)　(2007)　93　0-124].　In　this　paper,　we　study　the　global　structure　instability　of　the　Riemann　solution　u　=　U(x/t)　containing　shocks,　at　least　one　rarefaction　wave　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary.　We　prove　the　nonexistence　of　global　piecewise　C-1　solution　to　a　class　of　the　mixed　initial-boundary　value　problem　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　on　the　quarter　plane.　Our　result　indicates　that　this　kind　of　Riemarm　solution　u　=　U(x/t)　mentioned　above　for　General　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary　is　globally　structurally　unstable.　Some　applications　to　quasilinear　hyperbolic　systems　of　conservation　laws　arising　from　physics　and　mechanics　are　also　given.　(c)　2006　Elsevier　Inc.　All　rights　reserved.