Summary: Let \(A\) be a finite dimensional algebra over a field \(k\). We consider a subfunctor \(F\) of \(\text{Ext}^1_A(-,-)\), which has enough projectives and injectives such that \(\mathcal P(F)\) is of finite type, where \(\mathcal P(F)\) denotes the set of \(F\)-projectives. One can get the relative derived category \(D^b_F(A)\) of \(A\)-mod. For an \(F\)-self-orthogonal module \(T_F\), we discuss the relation between the relative quotient triangulated category \(D^b_F(A)/K^b(\mathrm{add\,}T_F)\) and the relative stable category of the Frobenius category of \(T_F\)-Cohen-Macaulay modules. In particular, for an \(F\)-Gorenstein algebra \(A\) and an \(F\)-tilting \(A\)-module \(T_F\), we get a triangle equivalence between \(D^b_F(A)/K^b(\mathrm{add\,}T_F)\) and the relative stable category of \(T_F\)-Cohen-Macaulay modules. This gives the relative version of a result of X.-W. Chen and P. Zhang [Manuscr. Math. 123, No. 2, 167-183 (2007; Zbl 1129.16011)].