  In this paper, we consider the twisted Hamiltonian extended affine Lie
algebra (THEALA). We classify the irreducible integrable modules for these Lie
algebras with finite-dimensional weight spaces when the finite-dimensional
center acts non-trivially. This Lie algebra has a triangular decomposition,
which is different from the natural triangular decomposition of twisted full
toroidal Lie algebra. Any irreducible integrable module of it is the highest
weight module with respect to the given triangular decomposition. In this
paper, we describe the highest-weight space in detail.
