Ray　nonsingular　matrices　are　generalizations　of　sign　nonsingular　matrices.　The　problem　of　characterizing　ray　nonsingular　matrices　is　still　open.　The　study　of　the　determinantal　regions　R(A)　of　ray　pattern　matrices　is　closely　related　to　the　study　of　ray　nonsingular　matrices.　It　was　proved　that　if　R(A)\{0}　is　disconnected,　then　it　is　a　union　of　two　opposite　open　sectors　(or　open　rays).　In　this　paper,　we　characterize　those　ray　patterns　whose　determinantal　regions　become　disconnected　after　deleting　the　origin.　The　characterization　is　based　on　three　classes　(F1),　(F2)　and　(F3)　of　matrices,　which　can　further　be　characterized　in　terms　of　the　sets　of　the　distinct　signed　transversal　products　of　their　ray　patterns.　Moreover,　we　show　that　in　the　fully　indecomposable　case,　a　matrix　A　is　in　the　class　(F1)　(or　(F2),　respectively)　if　and　only　if　A　is　ray　permutation　equivalent　to　a　real　SNS　(or　non-SNS,　respectively)　matrix.　(C)　2011　Elsevier　Inc.　All　rights　reserved.