The HP3458A has been well known as a high precision-type digital multimeter ͑DMM͒. However, when trying to identify any infinitesimally small ac signals as effective values, the existence of large residual noise appearing at the output reading when input signals to be measured are zero impedes the achievement of high precision to its full capability. This article shows that the greater part of the residual noise is produced as electronic noise from within the DMM and presents a trial of achieving high precision measurement by introducing a concept of noise decoupling. An equivalent zero noise state is searched for on one of the decoupled components by attaching an additional circuit in parallel and/or antiparallel to the input terminals and is found to be attainable with respect to the attached circuit. Consequently, possibilities of providing the full resolution to its capability and serving high precision measurement are discussed.