A 60-year-old worker was killed while moving a spider crane during construction of the £1.4 billion structure on 29 April.
The mans death is the first fatality at the site which began work in 2011.
Unite has now called on the Health and Safety Executive (HSE) to carry out a full investigation into the incident.
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Bernard MacAulay, the union's national officer for the construction sector, said: "Thirty-five construction workers lost their lives last year and there were over 65,000 reported workplace incidents that led to ill-health. That means that around one in four of those who lose their life at work is a construction worker. This is just unacceptable.
"Lessons must be learned because workers must be confident that they are working in safety, especially in construction which is already one of the most dangerous occupations in this country.
"There can never be any corners cut where health and safety is concerned. We need an urgent investigation into this tragic death at Queensferry, but it is crucial that trade unions play a part in that process of establishing the facts."
Work has been stopped on the bridge as investigations take place.
The £1.4bn structure is due to be completed by the end of this year.
(LM/CD)
