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The impact of spatiotemporal couplings (STCs) on the focal-spot intensity of ultra-intense femtosecond lasers scales up with the larger beam sizes and shorter pulse duration typically implemented to reach petawatt (PW) intensities. The repetition rate of such facilities (${ \lt }{10}\;{\rm Hz}$<10Hz) makes single-shot diagnosing of STCs mandatory. We present here a new, to the best of our knowledge, spatiotemporal diagnostic technique based on the comparison of the spatiospectral intensity of a pulse and its nonlinear third-order effect, in this case, cross-polarized wave generation (XPW), with an imaging spectrometer. The measured XPW spectrum displays specific couplings that depend on both amplitude and phase STCs of the initial pulse to be characterized. We confirm experimentally the ability of our new approach to diagnose common STCs in a laser pulse on the fly.