In this paper, first, we
introduce the new concept of 2-inner product on Banach modules over
a $C^*$-algebra. Next,  we present the concept of 2-linear operators
over a $C^*$-algebra. Our result improve  the main result of the
paper  Z. Lewandowska.  In the final of this paper, we
define the notions 2-adjointable mappings between 2-pre Hilbert
C*-modules and prove supperstability of them in the spirit of
Hyers-Ulam-Rassias.