Modal　properties　of　two-dimensional　(2D)　coupled　coherent　laser　array　have　been　investigated　based　on　coupled-mode　theory.　Block　tridiagonal　matrix　formalism　is　employed　to　present　the　coupling　matrix　and　calculate　array　supermodes　for　the　first　time.　Based　on　the　decomposition　of　the　block　tridiagonal　matrix,　analytical　descriptions　for　supermodes　in　N　x　N-element　array　with　lasers　coupling　their　nearest　and　second　nearest　neighbors　are　obtained.　According　to　the　near-and　far-field　distributions,　it　can　be　seen　that　although　the　number　of　supermodes　remains　NxN,　the　variety　of　intensity　profiles　is　reduced　to　N(N+1)/2.　In　addition,　the　maximum　wavelength　splitting　in　the　modes　is　estimated　from　the　coupling　strength　and　found　to　be　broadened　with　the　additional　couplings　that　take　place　along　the　two　diagonals,　which　will　contribute　to　supermode　selectivity.　Our　work　provides　a　new　method　for　future　research　on　2D　coherent　laser　arrays　under　a　variety　of　couplings　as　well　as　a　basis　for　supermode　engineering.