  The structure of superconducting order parameter near the surface of a
two-band superconductor with $s_{\pm}$ order parameter in the bulk is
theoretically investigated. The main parameter of the surface, which determines
the appropriate physics is the coefficient of the interband scattering
$R_{12}$. For small $R_{12}$ the superconducting order parameter is only
suppressed to some extent near the surface for the both bands. For intermediate
and strong interband scattering there are two possible non-trivial surface
states of the order parameter: (i) purely real solution, where the symmetry of
the superconducting state near the surface is changed from $s_{\pm}$ to
conventional $s_{++}$ and (ii) time-reversal symmetry breaking (TRB) state. In
this state the order parameters in the two bands acquire phases $\phi_{1,2}(x)
\neq (0,\pi)$ upon approaching the surface. We argue that at low temperatures
the TRB surface state can be more energetically favorable than the $s_{\pm} \to
s_{++}$ time reversal symmetry conserving state (TR). For higher temperatures
up to $T_c$ only the TR state can exist. The transition between the two
temperature regions is rather sharp. Signatures of the transition between the
TRB and the TR surface states can be detected by the measurements of the local
density of states and the angle-resolved density of states.
