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We study two-component surface solitons in a pair of linearly coupled truncated waveguiding arrays with the Kerr nonlinearity. Symmetric solitons have a very small stability area, while those that are antisymmetric and asymmetric are stable in vast regions. Below a critical value of the coupling constant, branches of the symmetric and asymmetric modes separate, and accordingly, asymmetric solitons cease to bifurcate from the symmetric ones, providing the first example of asymmetric modes indoi:10.1364/ol.38.001064 pmid:23546244 fatcat:gxn3u3dbived5pv5ofaerxovba