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We establish necessary and sufficient conditions for the stability of thefinite section method for operators belonging to a certain $C^*$-algebra ofoperators acting on the Hilbert space $l^2_H(\mathbb{Z})$ of $H$-valuedsequences where $H$ is a given Hilbert space. Identifying $l^2_H(\mathbb{Z})$with the $L^2_H$-space over the unit circle, the $C^*$-algebra in question isthe one which contains all singular integral operators with flip and piecewisequasicontinous $\mathcal{L}(H)$-valued generating functions on the unit circle.The result is a generalization of an older result where the same problem, butwithout the flip operator was considered. The stability criterion is obtainedvia $C^*$-algebra methods and says that a sequence of finite sections is stableif and only if certain operators associated with that sequence (via$^*$-homomorphisms) are invertible.

Finite Section Method for singular integrals with operator-valued PQC-coefficients and a flip