  Every link is shown to be presentable as a boundary of an unknotted flat
banded surface. A (flat) banded link is defined as a boundary of an unknotted
(flat) banded surface. A link's (flat) band index is defined as the minimum
number of bands required to present the link as boundaries of an unknotted
(flat) banded surface. Banded links of small (flat, respectively) band index
are considered here. Some upper bounds are provided for these band indices of a
link using braid representatives and canonical Seifert surfaces of the link.
The relation between the band indices and genera of links is studied and the
band indices of pretzel knots are calculated.
