  The Izergin-Korepin model with general non-diagonal boundary terms, a typical
integrable model beyond A-type and without U(1)-symmetry, is studied via the
off-diagonal Bethe ansatz method. Based on some intrinsic properties of the
R-matrix and the K-matrices, certain operator product identities of the
transfer matrix are obtained at some special points of the spectral parameter.
These identities and the asymptotic behaviors of the transfer matrix together
allow us to construct the inhomogeneous T-Q relation and the associated Bethe
ansatz equations. In the diagonal boundary limit, the reduced results coincide
exactly with those obtained via other methods.
