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Transient current (IDD) testing has been often cited and investigated as an alternative and/or supplement to quiescent current (IDDQ) testing. In this correspondence, we present a novel integrated method for fault detection and localization using wavelet transform-based IDD waveform analysis. The time-frequency resolution property of wavelet transform helps us detect as well as localize faults in digital CMOS circuits. Experiments performed on measured data from a fabricated 8-bit shift register, and simulation data from more complex circuits show promising results for both detection and localization. Wavelet-based detection method shows better sensitivity than spectral and time-domain methods. Effectiveness of the localization method in presence of complex power supply network, measurement noise, and process variation is also addressed.