  We present two methods for constructing a flat band (FB) system having a flat
energy dispersion over the entire Brillouin zone within tight-binding model,
where the resulting Hamiltonian may not be easily obtained by existing methods
based on a bipartite graph and line graph techniques. In the first method, we
derive a set of conditions equivalent to the appearance of FBs for a given
graph structure. This method allows parameter to be tuned so that systems with
a small number of sites per unit cell has a FB. In the second method, we show
that FB systems can be obtained by removing or adding sites to an existing FB
system under specific rules. In particular, the site addition method enables us
to construct multiple FB systems stemming from a single FB system. The FB
system obtained by the second method has the characteristics that the component
ratios in the FB eigenstate are partially common to the original system. We
illustrate how lattices having a FB can be constructed by applying the latter
method starting from an existing lattice such as a kagome lattice,
demonstrating that a wide variety of lattices can possess a FB in the band
structure.
