We have investigated thermal expansion of a tetragonal Mn(88)Ni(12) alloy by x-ray diffraction, Mn and Ni K-edge extended x-ray-absorption fine-structure spectroscopy, and the computational simulations based on the path-integral effective-classical-potential theory. It is found from the x-ray diffraction that the tetragonal lattice constant c exhibits almost no thermal expansion like an Invar alloy, while the lattice constant a shows even larger thermal expansion than usually expected from anharmonicity, implying significant anisotropy in thermal expansion. The extended x-ray-absorption fine-structure reveals that the Mn local environment is actually tetragonally distorted, while the Ni one retains its inherent cubiclike symmetry. Combined with the computational simulations, it is concluded that large thermal expansion along the a axis originates from the anti-Invar effect, while negligibly small thermal expansion along the c axis originates from the cooperative Invar effect. Namely, the tetragonally distorted more stable antiferromagnetic Mn state gives a significantly smaller (slightly longer) atomic radius along the a (c) axis than the radius of the spherical paramagnetic state.