  Negabent functions were introduced as a generalization of bent functions,
which have applications in coding theory and cryptography. In this paper, we
have extended the notion of negabent functions to the functions defined from
$\mathbb{Z}_q^n$ to $\mathbb{Z}_{2q}$ ($2q$-negabent), where $q \geq 2$ is a
positive integer and $\mathbb{Z}_q$ is the ring of integers modulo $q$. For
this, a new unitary transform (the nega-Hadamard transform) is introduced in
the current set up, and some of its properties are discussed. Some results
related to $2q$-negabent functions are presented. We present two constructions
of $2q$-negabent functions. In the first construction, $2q$-negabent functions
on $n$ variables are constructed when $q$ is an even positive integer. In the
second construction, $2q$-negabent functions on two variables are constructed
for arbitrary positive integer $q \ge 2$. Some examples of $2q$-negabent
functions for different values of $q$ and $n$ are also presented.
