In dual assembly component mode synthesis, interconnecting forces between substructures are handled using Lagrange multipliers. These methods offer the advantage of allowing the interconnecting force to be calculated explicitly through the augmented Lagrange multiplier into the variable vector. However, this augmentation entails additional degrees of freedom (DOFs), leading to rank-deficiency in the system matrix and increased computational cost. Furthermore, such rank-deficiency creates potential for numerical instability. This study condenses the augmented variable in flexibility-based component mode synthesis by adopting the variable condensation scheme of the displacement-partitioned method. This variable condensation extends to interface DOFs, resulting in a highly compact model. Distinct from other interface reduction methods that suffer from accuracy loss, the proposed scheme yields more accurate results than the original model while avoiding null-space problems, thus demonstrating superior numerical robustness.