The Response business has been sold for an undisclosed sum to a management buyout team headed by managing director Brian Bannatyne, who has been leading efforts to improve performance at the firm since 2009.
The sale follows a challenging period for the business, which employs around 1,500 people in Glasgow.
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Response was hit hard in 2012 when the company lost a key sales and support contract with Sky that around 950 people worked on.
The disposal is the latest in a series completed by Murray International Holdings to raise funds the company could use to pay off the huge debts it built up during the boom that ended with the credit crunch in 2007.
Murray International Holdings became one of the biggest Scottish debtors of the former Bank of Scotland.
In April last year Sir David said the group was "doing the honourable thing" by the bank and would sell assets in order to return as much as it could.
He noted that Murray family interests had bought out the group's steel business and had become bigger than that group, which he described as a legacy business.
In December 2012 Murray International Holdings offloaded Premier Hytemp, its North Sea-focused speciality steel business, in a £34.5 million buyout led by former managing director Donald Wilson.
The latest accounts for Murray International Holdings show the group reduced its debt pile by £23.3m in the year ended 30 June 2013, to £347m. In the accounts, Sir David spoke of his "profound regret" over the decision to sell his majority shareholding in Rangers football club to Scots businessman Craig Whyte in 2011.
The latest accounts for Response (Building Rewarding Relationships) show the company made an operating loss of £484,000 on sales of £28.3 million in the year to June 30 2012. It made £28,000 profit on £32m sales in the preceding year.
A spokesman for Response, who confirmed the MBO had been completed, said the accounts to June 30 2013 will be filed imminently and business performance has been strong.
He added: "We are now looking forward to building upon the excellent progress that the business has made, whilst realising our unique vision of developing a very different type of contact centre."
A spokesman for Murray International Holdings said: "The business has been sold following a long and quite detailed process," without giving details.
Mr Bannatyne was appointed managing director of Response in 2009 to lead an overhaul of its organisational structure and corporate strategy.
Before joining Response he had senior roles with Semple Cochrane, the Scottish engineering group and America's Honeywell Corporation
The MBO team also includes Andrew Harvey, Reponse's operations director; John Goodram, director of technology; Arceeb Moughal, director of client partnerships, and Julie McIntosh, director of people and culture.