  In typical flat-band models, defined as nearest-neighbor tight-binding
models, flat bands are usually pinned to the special energies, such as top or
bottom of dispersive bands, or band-crossing points. In this paper, we propose
a simple method to tune the energy of flat bands without losing the exact
flatness of the bands. The main idea is to add farther-neighbor hoppings to the
original nearest-neighbor models, in such a way that the transfer integral
depends only on the Manhattan distance. We apply this method to several lattice
models including the two-dimensional kagome lattice and the three-dimensional
pyrochlore lattice, as well as their breathing lattices and non-line graphs.
The proposed method will be useful for engineering flat bands to generate
desirable properties, such as enhancement of $T_c$ of superconductors and
nontrivial topological orders.
