We have investigated the role of surface steps in the arrangement of silicon nano-dots on a vicinal Si(111) surface by scanning tunneling microscopy. Nanometer sized silicon nitride islands were formed on a vicinal Si(111) surface, which was 1degrees off toward [(1) over bar(1) over bar2] direction, via thermal nitridation using N-2 gas. On the nitrided surface, oxygen gas was dosed to induce a local selective etching of bare silicon using the silicon nitride islands as masks. The resultant surface showed one-dimensional arrangement of silicon nano-dots along the step edges of silicon surface. The lateral size of the dot in the direction perpendicular to the step edges was restricted to the terrace width of the stepped Si(111) surface. We consider that the preferential growth of silicon nitride islands on the edges of single height steps is responsible for the arrangement of silicon nano-dots along the step edges of the 1degrees off vicinal Si(111) surface.