Here’s an extract from the postscript that will answer that question:
In this book we sought to build a picture of the historical origins of the Gospels based on the tradition preserved for us in the patristic writings. In particular, we were concerned with the attempt in the early church to explain the distinctive nature of the Gospel according to Mark. Two significant points have emerged from our study. First, Mark’s Gospel is best seen as the result of the cooperation between Peter and Paul to ensure that the unity of the early church was not impaired as a result of the publication of the Gospel of Luke alongside the Gospel of Matthew. In other words, the Gospel of Mark was never intended to be a rival of Matthew and Like, for its purpose was a very limited one, namely to provide the approbation necessary for Luke to find general acceptance in all the churches, both east and west. Second, the Gospel of Mark is best understood as Peter’s declaration that Luke is faithful to the apostolic tradition. The Gospel of Mark is therefore to be seen as the necessary link between the Gospels of Matthew and Luke. This fact alone explains the supposed contradiction between Clement’s assertion that Matthew and Luke were written before Mark and the canonical order Matthew-Mark-Luke, for it is possible for Mark to be regarded as both second and third – third in order of actual composition, and second in order of authority as the work of Peter.