Cai　and　Zhang　establish　separate　perturbation　bounds　for　sin　Theta　distances　with　spectral　and　Frobenius　norms　(Cai　T,　Zhang　A.　Rate-optimal　perturbation　bounds　for　singular　subspaces　with　applications　to　high-dimensional　statistics.　The　Annals　of　Statistics.　2018;　Vol.　46,　No.　1:　60-89).　We　extend　their　theorem　to　each　unitarily　invariant　norm.　It　turns　out　that　our　estimation　is　optimal　as　well.