Deputy chairman Dato' Dr Ramli bin Mohamad, of large Malaysian shareholder Intria, has taken over until a new chairman is appointed.
Outgoing chief executive John Armitt maintained that Beckett's departure would not affect Costain, despite its coming two months after he announced his own retirement.
He said: "The business sails along. Michael had been in the job for three months and had not had time to have an impact on the business. So, in a way, if you are going to lose a chairman it is better after three months rather than a year or 18 months."
Finance director Miles Roberts said he was disappointed by Beckett's departure but added that the search for his replacement was already under way and that Costain hoped to make an announcement shortly. He also said the group was looking to appoint three more independent non-executive directors soon.
If you are going to lose a chairman it is better after three months than a year
John Armitt, Costain
Armitt also revealed that Costain was considering following Carillion and WS Atkins' example by appointing an industry outsider chief executive.
He said: "We've had a look at a couple of people from outside the industry and one or two from within the industry." He said that, although Costain had not yet narrowed down its choices, he was hopeful that an announcement would be made in the next two weeks.
As for his own future, Armitt said he had received a number of offers but had not discussed any of these in depth. He refused to comment on speculation linking him to jobs at Railtrack or Alfred McAlpine.
He said: "When I leave, I'll be taking a bit of time to rest and then we'll see what happens and what offers there are." When he announced his resignation, Armitt said he expected to stay in the industry.
