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In this paper, one new integrable modified extended Toda hierarchy(METH) isconstructed with the help of two logarithmic Lax operators. With thismodification, the interpolated spatial flow is added to make all flowscomplete. To show more integrable properties of the METH, the bi-Hamiltonianstructure and tau symmetry of the METH will be given. The additional symmetryflows of this new hierarchy are presented. These flows form an infinitedimensional Lie algebra of Block type.

Additional symmetry of the modified extended Toda hierarchy