Map　joining　is　an　efficient　strategy　for　solving　feature　based　SLAM　problems.　This　paper　demonstrates　that　joining　of　two　2D　local　maps,　formulated　as　a　nonlinear　least　squares　problem　has　at　most　two　local　minima,　when　the　associated　uncertainties　can　be　described　using　spherical　covariance　matrices.　Necessary　and　sufficient　condition　for　the　existence　of　two　minima　is　derived　and　it　is　shown　that　more　than　one　minimum　exists　only　when　the　quality　of　the　local　maps　used　for　map　joining　is　extremely　poor.　The　analysis　explains　to　some　extent　why　a　number　of　optimization　based　SLAM　algorithms　proposed　in　the　recent　literature　that　rely　on　local　search　strategies　are　successful　in　converging　to　the　globally　optimal　solution　from　poor　initial　conditions,　particularly　when　covariance　matrices　are　spherical.　It　also　demonstrates　that　the　map　joining　problem　has　special　properties　that　may　be　exploited　to　reliably　obtain　globally　optimal　solutions　to　the　SLAM　problem.　©　2012　IEEE.