We measure the large-scale intrinsic alignments of galaxy clusters in the Sloan Digital Sky Survey (SDSS) using subsets of two cluster catalogues: 6625 clusters with 0.1 < z < 0.3 from the maxBCG cluster catalogue (7500 deg2) and 8081 clusters with 0.08 < z < 0.44 from the adaptive matched filter catalogue (6500 deg2). We search for two types of cluster alignments using pairs of clusters: the alignment between the projected major axes of the clusters (‘correlation’ alignment), and the alignment between one cluster major axis and the line connecting it to the other cluster in the pair (‘pointing’ alignment). In each case, we use the cluster member galaxy distribution as a tracer of the cluster shape. All measurements are carried out with each catalogue separately to check for dependence on cluster selection procedure. We find a strong detection of the pointing alignment on scales up to 100 h−1 Mpc, at the 6σ or 10σ level depending on the cluster selection algorithm used. The correlation alignment is only marginally detected up to ∼20 h−1 Mpc, at the 2σ or 2.5σ level. These results support our current theoretical understanding of galaxy cluster intrinsic alignments in the Λ cold dark matter paradigm, although further work will be needed to understand the impact of cluster selection effects and observational measurement errors on the amplitude of the detection.