A new idea of approximating a high order linear system by a low order model generated via a nearby non-minimal system in the parameter space is suggested. The approximation criterion is established on the basis of the topological notions called near-uncontrollability and near-unobservability. To obtain a joint measure for these two ‘abilities’, the parameter symmetric realizations and parametric balanced realizations are defined. Some theoretical results concerning the problems of parameter symmetrization, parametric balancing and near-uncontrollability/near-unobservability decomposition are derived. A model reduction algorithm based on these results is proposed with an illustrative example.