A source close to Rok said: "Rok has always said it looks to turn around underperforming construction businesses, but Galliford Try has turned the division around."
Rok's interest is known to have waned in recent months, and it signalled its intentions by lowering its stake from 3% to less than 2%.
Galliford Try's construction division has improved under the leadership of former Skanska executive Andy Sturgess. Its operating profit in the second half of last year was £2m from a £269m turnover. The division was in the red before Sturgess' arrival.
Galliford Try's interim results for the company as a whole, released last week, show a 75% increase in pre-tax profit to £9.6m. Turnover rose 19% to £354m. The interim dividend was 0.55p, compared with 0.5p last year.
Chairman Tony Palmer said: "Housebuilding continues to perform well and we are on track with our objective to increase margins in construction."