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The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain and tree multibody systems with the transfer matrix method for multibody systems. However, for linear multibody systems with closed loops, the recursive relations of the Riccati transfer matrices are yet to be established. Therefore, it is difficult to compute linear multibody systems with closed loops using the RTMM. In this paper, a new Riccati transformation for such systems is established by transforming the system into a derived tree system by cutting the closed loops. An RTMM formalism for general linear multibody systems with closed loops is then formulated based on the chain and tree multibody systems. The steady-state response under harmonic excitation is taken as an example to validate the proposed method.