Unlike the algorithms for convex polygon triangulation which make the triangulation of an n-gon from the scratch, we propose the algorithm making the triangulation of an (n+1)-gon on the base of already found triangulations of an n-gon. For such a purpose we must maintain suitable file storage to store previously derived triangulations and later use them to generate the triangulations of polygon with one more vertex. The file storage is partially exploited for elimination of duplicates our algorithm produces. Yet, triangulation and elimination of duplicates do not critically decrease our algorithm performances for smaller values of n
