  We investigate the deformation of involution and multiplication in a unital
$C^*$-algebra when its norm is fixed. Our main result is to present all
multiplications and involutions on a given $C^*$-algebra $\mathcal{A}$ under
which $\mathcal{A}$ is still a $C^*$-algebra whereas we keep the norm
unchanged. For each invertible element $a\in\mathcal{A}$ we also introduce an
involution and a multiplication making $\mathcal{A}$ into a $C^*$-algebra in
which $a$ becomes a positive element. Further, we give a necessary and
sufficient condition for that the center of a unital $C^*$-algebra
$\mathcal{A}$ is trivial.
