This paper proposes a novel scheme for the generation of primary residual vector (PRV) for sensor fault detection and isolation (FDI) in multivariate systems. The PRV is made insensitive to process uncertainties, including model-plant mismatch (MPM) and process disturbances. To generate the PRV, we do not need a precise system model. Instead, all we need is an estimate of the system model, which may be biased from the true model. Under the condition that the number of process uncertainties is less than the number of outputs, the generated PRV can be made perfectly insensitive to process uncertainties. Even when this condition does not hold, the most important elements in the process uncertainties can still be decorrelated with the PRV. A numerical example to demonstrate the theory is given. The newly proposed approach is compared with existing robust FDI schemes, e.g., the Chow-Willsky scheme.