In this work, we demonstrate that the zero-fidelity, an approximation to the process fidelity, when combined with randomized benchmarking, becomes robust to state preparation and measurement (SPAM) errors. However, as randomized benchmarking requires randomly choosing an increasingly large number of Clifford elements from the Clifford group when the qubit number increases, this combination is also limited to quantum systems with up to three qubits. To make the zero-fidelity independent of SPAM errors and, at the same time, applicable to multi-qubit systems, we employ a channel noise scaling method similar to the method of global unitary folding, or identity scaling, used for quantum error mitigation.