The instability of Wi-Fi received signal strength (RSS) incurred by mutable channel characteristics hampers a wide-spread adoption of RSS based location fingerprinting to real world indoor localization applications. To overcome RSS instability, we propose a new approach based on the concept of "invariant RSS statistics". By invariant RSS statistics, we mean the RSS samples collected at each calibration location, especially, under minimal random spatiotemporal disturbances. The proposed method forms the reference pattern classes for individual calibration locations with the invariant RSS statistics thus obtained. Fingerprinting is done by identifying the reference pattern class that maximally supports the RSS readings collected at an unknown location for available Wi-Fi sources. The support of RSS readings is defined here as the sum of the likelihood probabilities of individual RSS readings. Unlike conventional methods, the proposed method allows only those readings high in statistical confidence to participate in the sum, while excluding other readings. This is to screen out the influence of those readings contaminated by time-varying disturbances on classification. Experimental results show that the proposed method provides superior performance to conventional ones with the success rate higher by 17%, the printing resolution finer by 30% and, naturally, no performance degradation in time without recalibration.