  Based on the parallelogram law and isosceles orthogonality, we define a new
orthogonal geometric constant. We first discuss some basic properties of this
new constant. Next, we consider the relation between the constant and the
uniformly non-square property. Moreover, a generalized constant is also
introduced and some basic properties are presented. It is shown that, for a
normed space, the constant value is equal to 1 if and only if the norm can be
induced by the inner product. Finally, we verify that this constant is closely
related to the well-known geometric constants through some inequalities.
