The method for detection of the galaxy cluster rotation based on the study of distribution of member galaxies with velocities lower and higher of the cluster mean velocity over the cluster image is proposed. The search for rotation is made for flat clusters with $a/b>1.8$ and BMI type clusters which are expected to be rotating. For comparison there were studied also round clusters and clusters of NBMI type, the second by brightness galaxy in which does not differ significantly from the cluster cD galaxy. Seventeen out of studied 65 clusters are found to be rotating. It was found that the detection rate is sufficiently high for flat clusters, over 60\%, and clusters of BMI type with dominant cD galaxy, ~ 35%. The obtained results show that clusters were formed from the huge primordial gas clouds and preserved the rotation of the primordial clouds, unless they did not have merging with other clusters and groups of galaxies, in the result of which the rotation has been prevented.

6 pages, 17 figures