Cross-correlation (CC) determined relative time delays, or related differential travel times, between pairs of seismic events at the same station are often used as input data to improve earthquake relocation results. Researchers generally select those time delays with associated CC coefficients larger than a chosen threshold. When two similar time series are contaminated by correlated noise sources, the relative time delay between them calculated with the CC technique is sometimes not reliable. Noise sources at a station for different events can be partially correlated or just randomly correlated. In this work, we use the bispectrum (BS) method, which works in the third-order spectral domain, to check the reliability of the CC determined time delay. We calculate two time delays with the BS method, one using the bandpass-filtered waveforms and the other with the raw data, and use them to verify (select or reject) the CC estimate computed with the filtered waveforms. We apply this technique to obtain bispectrum-verified CC differential times for 822 New Zealand earthquakes in the Wellington area. Our work demonstrates that the CC time delays verified with the BS method provide improved (smaller root mean square residual and more clustered) earthquake relocation results compared to those selected with the standard threshold criterion.