In this paper, we examine time-varying correlations among stock returns of Apple, Microsoft, Amazon and Google. Employing a multivariate DCC-GARCH model, we find that there are strong linkages among these four assets. Starting from lower levels, correlation values for most asset pairs exhibit a stable ascending movement in recent upward trended markets to, in an exceptional case, almost hit the perfect positive correlation mark. We show that correlations among these assets jump during downturn market periods, suggesting limits in the diversification of risk within the segment of large cap U.S. technology stocks. Our results are helpful for portfolio management and asset allocation.