  In this paper, it is shown that, for any equidimensional $C^\infty$ map-germ
$f: (\mathbb{R}^n,0)\to (\mathbb{R}^n,0)$, the map-germ $F: (\mathbb{R}^n, 0)
\to \mathbb{R}^n\times\mathbb{R}^{\ell}$ defined by $F(x)=\left(f(x),
\mu_1(x){|Jf|^2(x)}, \cdots, \mu_\ell(x){|Jf|^2(x)}\right)$ is always a
frontal; where $\mu_i$ is a $C^\infty$ function-germ and $|Jf|$ is the
Jacobian-determinant of $f$. Moreover, it is also shown that when the
multiplicity of $f$ is less than or equal to $3$, any frontal constructed from
$f$ must be $\mathcal{A}$-equivalent to a frontal $F$ of the above form.
