We present the result of a search for correlations in the arrival times of high energy muons collected from 1995 till 2000 with the streamer tube system of the complete MACRO detector at the underground Gran Sasso Lab. Large samples of single muons (8.6 million), double muons (0.46 million) and multiple muons with multiplicities from 3 to 6 (0.08 million) were selected. These samples were used to search for time correlations of cosmic ray particles coming from the whole upper hemisphere or from selected space cones. The results of our analyses confirm with high statistics a random arrival time distribution of high energy cosmic rays. (c) 2005 Elsevier B.V. All rights reserved.