In this paper, we show explicitly the existence of lccalized vibrations, and give some discussions on the localized vibration in a finitely extended system of linear harmonic oscillators, especially in relation to the Schrödinger coordinates. A locally reduced mass, lccal strong interactions between particles, or an applied external force of high frequency, froms the cause of the existence of the localized vibration in the finitely extended system. The range of the extention of the localized vibration is also discussed briefly, being based on the Schrbdinger coordinates.