System combination or fusion is a popular, successful and sometimes straightforward means of improving performance in many fields of statistical pattern classification, including speech and speaker recognition. Whilst there is significant work in the literature which aims to improve speaker diarization performance by combining multiple feature streams, there is little work which aims to combine the outputs of multiple systems. This paper reports our first attempts to combine the outputs of two state-of-the-art speaker diarization systems, namely ICSI's bottom-up and LIA-EURECOM's top-down systems. We show that a cluster matching procedure reliably identifies corresponding speaker clusters in the two system outputs and that, when they are used in a new realignment and resegmentation stage, the combination leads to relative improvements of 13% and 7% DER on independent development and evaluation sets.