  The notion of normal category was introduced by KSS Nambooripad in connection
with the study of the structure of regular semigroups using cross
connections\cite{nambooripad1994theory}. It is an abstraction of the category
of principal left ideals of a regular semigroup. A normal band is a semigroup
$B$ satisfying $a^2=a$ and $abca=acba$ for all $a,b,c \in B$. Since the normal
bands are regular semigroups, the category $\mathcal{L}(B)$ of principal left
ideals of a normal band $B$ is a normal category. One of the special properties
of this category is that the morphism sets admit a partial order compatible
with the composition of morphisms. In this article we derive several properties
of this partial order and obtain a new characterization of this partial order.
