Presently,　substantial　studies　have　been　conducted　to　investigate　periodicities　hidden　in　biological　sequences.　Among　them,　the　Self-Adaptive　Spectral　Rotation　(SASR)　method　is　said　to　be　an　efficient　tool　to　visualize　the　3-bp　periodicity　(TP)　in　DNA　sequences.　It　outputs　a　random　walk,　i.e.,　TP　walk,　in　the　complex　plane　for　any　query　sequence.　And　the　TP-intensive　regions　in　the　sequence　can　be　visually　discriminated　from　the　non-TP　ones　in　the　walk.　In　this　paper,　the　behaviors　of　the　walks　for　non-TP　sequences　are　further　investigated　qualitatively.　A　slightly　leftward　trend　(an　abnormity)　in　such　walks　is　observed,　which　is　not　reported　in　the　previous　SASR　literatures.　An　improved　SASR,　named　the　mature　SASR,　is　proposed,　in　order　to　eliminate　the　abnormity,　correct　the　TP　walks,　and　provide　a　better　visualization.　©　2014　IEEE.