The relationship between the chairman and the chief executive of a company is absolutely fundamental according to Sir David Walker, former chairman of Barclays, speaking on Radio 4's, The Bottom Line.

In a discussion about managing the boardroom, Michael Jackson, venture capitalist and former chair of Sage Group, said the main role of the chair is to back or fire the chief executive. Walker largely agreed in this analysis saying that chairs of boards have a critical role in identifying, recruiting, mentoring, helping and appraising chief executives. The relationship between the two people needs to be based on trust between them and if there was trust there could be disagreements between them.

However, Walker added, "If the chairman and the chief executive don't get on, and that persists, one of them will have to go."

Margaret Heffernan, a former chief executive (CEO) and author who has also served as a non-executive director, cautioned that the role of questioning and challenging the chief executive should not just fall to the chair. Hefferman said that every member of a board has their own blind spots to certain issues that might weaken a company and this includes the chair and chief executive and they could have their own blind spots. The wider board therefore needed to be able to challenge them both of them.

Heffernan said, "On most boards I have sat on the CEO and the chair have wanted to agree". She said the role of the board in that case was to test the company strategy they are working on to ensure that it "holds water".

Talking about the board meetings Jackson said the piece of advice he followed was to always talk about the most important things first and then the next most important things. Hefferman agreed that some chief executives bury thorny issues.

Walker, who carried out a review of the corporate governance of banks in the wake of the 2008 financial crash, said he found - and this applied more widely than just the banks - that there had been an amateurism in the boardrooms among the non-executive directors (NED) and there had been an abdication of their responsibilities. It was only now being recognised, he said, that major companies have a huge influence on the well-being and health of society matched only by elected representative and regulators. This recognition was bringing more professionalism in to the role of the NED.

NEDs on the  boards of major companies, it was agreed, needed to spend two or three days a month on their role and a monthly board meeting was generally necessary. A diverse range of people was also required. Jackson said as an entrepreneur he was more interested in the talent of young business people than their gender although he admitted three of his best CEOs had been women. Walker suggested three three types of people that were needed on boards - those with knowledge of transactions such as mergers and acquisitions, people with specific professional experience related to the business sector of the company and also those with "L-plates".

While at Barclays Walker had been keen for executives from the bank to become NEDs on elsewhere and for executives from other companies to serve on his board as NEDS, "otherwise experience can't be accumulated", he said.

Heffernan said that so-called charismatic chief executives are a 'gigantic problem' in respect of ensuring a successful company as they have been shown to drive volatility in business and, "Nobody wants to stand up to them and challenge them." Walker added that he felt four or five years were good lengths of time for a chief executive to have their role - after that time company executives became to assailable to be challenged from employees below them or by the executive committee and also ceased to be challenged in the boardroom.

In an earlier discussion on ethics and corporate governance at the recent World Economic Forum annual meeting Lucy Marcus, CEO of Marcus Venture Consulting who has served on company boards, said they were becoming less opaque than in the past. Before there had been a tendency towards the cult of the CEO but now people scrutinised the role of all the board and board meetings. Social media she said had helped in providing more scrutiny of the boardroom.

The chair of a board sets its tone and good chemistry between the board members was important. It was important for NEDs to understand their role - to be ready to be educated about the company and that they should be 'hands on, not hands in.

Barbara Novick, vice chairman of investment firm BlackRock, said that as much of its money invested was in passive funds - so divestment of shares was not an option -  it  felt a strong obligation to engage with companies on issues of concern and to ask hard questions of company boards rather than just voting against issues at company meetings although Novick said this was an option they could take. She said last year BlackRock engaged with around 1500 companies.