  The localized nature of a flat band is understood by the existence of a
compact localized eigenstate. However, the localization properties of a
partially flat band, ubiquitous in surface modes of topological semimetals,
have been unknown. We show that the partially flat band is characterized by a
non-normalizable compact localized state(NCLS). The partially flat band
develops only in a momentum range, where normalizable Bloch wave functions can
be obtained by the linear combination of the NCLSs. Outside this momentum
region, a ghost flat band, unseen from the band structure, is introduced for
the consistent counting argument with the full set of NCLSs. Then, we
demonstrate that the Wannier function corresponding to the partially flat band
exhibits an algebraic($\sim 1/r^{1+\epsilon}$ in 1D and $\sim
1/r^{3/2+\epsilon}$ in 2D) decay behavior, where $\epsilon$ is a positive
number. Namely, one can have the Wannier obstruction even in a topologically
trivial band if it is partially flat. Finally, we develop a construction scheme
of a tight-binding model of the topological semimetal by designing an NCLS.
