The reason given is the scaling down of the organisation resulting from the sale of its training subsidiary ReMIT and subsequent reduction in RMIF staff numbers from 400 to 50.
In a statement the organisation said it was looking for a more ‘federal structure’ and was there a ‘diminution in the requirement for a chief executive’.
RMIF president Keith Sayfritz said: "As a consequence of the ReMIT sale and thanks to Carrington's outstanding work, the RMIF can now look to the future with confidence. It has resolved its long term financial problems. It has an endowment fund to support its future work on behalf of members and has eliminated its pension fund deficit. Under his leadership, the RMIF has become the ‘voice of the retail motor industry’ and is well on the way towards developing an outstanding range of high quality member services.
"The Board wishes to express its gratitude to Matthew for his immense achievements in delivering financial strength to the RMIF, in modernising the delivery of its services, in building strong teams to assist members and in making the RMIF very successful in representing its members' views to government and other outside bodies.
"On behalf of the RMIF Board, I wish to thank Matthew personally for his hard work and dedication to the RMIF during the nearly five years he has led the organisation. We wish him every success for the future."
Carrington said: "It has been a privilege to serve as the chief executive of the RMIF since 2002. I wish to thank the members of the trade associations which make up the federation for the help and support they have given to me during this time. Also, my thanks go to the members of the RMIF staff who have been highly professional and dedicated in the work we have carried out together as a team."
Kevin Waterman, RMIF finance director, will serve as the group's interim managing director from November 1.