This paper considers the effect of the carrier phase error on the probability of error in a binary quadrature amplitude modulation (QAM) data transmission system in the presence of intersymbol interference and additive Gaussian noise. The analysis shows that there exists a threshold value of the carrier phase error such that the error probability remains almost unchanged as long as the carrier phase error is less than that threshold value, but increases rapidly once the threshold is exceeded. Good agreement between theory and computer simulations is obtained. Some practical implications of this threshold effect are discussed.