  In this paper, we introduce a method, called a plat form, of describing a
surface-link in the 4-space using a braided surface. We prove that every
surface-link, which is not necessarily orientable, can be described in a plat
form. The plat index is defined as a surface-link invariant, which is an
analogy of the bridge index for a link in the 3-space. We classify
surface-links with plat index $1$ and show some examples of surface-links in
plat forms.
