  Recently it has been shown that the theory in the quadratic gauge on
4-sphere, $\mathbb{S}^{4}$ consists of two phases namely, the confined and the
deconfined phases. A suitable finite field dependent BRST (FFBRST)
transformation interrelates two different gauge fixed theories. In this paper,
we use the FFBRST technique on the curved space for the first time and
elaborate a novel application of it. We propose two different formulations of
this technique that transform the deconfined phase action on sphere to the
confined phase action on sphere inside the quadratic gauge. Both proposed
passages change the phase with BRST invariance to the phase without BRST
invariance unlike usual connections where the FFBRST operation leave the BRST
symmetry intact and there is a unique field theoretic essence of them, which
makes them particularly important to study. Thus, the two different field
redefinitions act as a new mechanism that execute phase transition between two
real QCD phases on 4-sphere other than ghost condensation process.
