We　investigate　the　existence　of　a　global　classical　solution　to　the　Goursat　problem　for　linearly　degenerate　quasilinear　hyperbolic　systems　of　diagonal　form.　As　the　result　in　[A.　Bressan,　Contractive　metrics　for　nonlinear　hyperbolic　systems,　Indiana　Univ.　Math.　J.　37　(1988)　409-421]　suggests　that　one　may　achieve　global　smoothness　even　if　the　C-1　norm　of　the　initial　data　is　large,　we　prove　that,　if　the　C-1　norm　and　the　BV　norm　of　the　boundary　data　are　bounded　but　possibly　large,　then　the　solution　remains　C-1　globally　in　time.　Applications　include　the　equation　of　time-like　extremal　surfaces　in　Minkowski　space　R1+(1+n)　and　the　one-dimensional　Chaplygin　gas　equations.