In　this　paper,　two　new　properties　of　singular　value　decomposition　(SVD)　on　images　are　proved.　The　first　property　demonstrates　the　quantitative　relationship　between　singular　values　and　power　spectrum.　The　second　one　proves　that　under　the　condition　of　losing　equal　power　spectrum,　the　square-error　of　the　reconstructed　image　is　much　smaller　when　we　reduce　all　singular　values　proportionally　instead　of　neglect　the　smaller　ones.　Based　on　the　two　properties,　a　new　data-hiding　scheme　is　proposed.　It　performs　well　as　for　robustness,　for　it　satisfies　power-spectrum　condition　(PSC),　and　PSC-compliant　watermarks　are　proven　to　be　most　robust.　Besides,　the　proposed　scheme　has　a　good　performance　as　for　capacity　and　adaptability.