Construction firm Carillion has officially pulled out of the running for a merger with rival Balfour Beatty after yet another rejection by the infrastructure specialist on Wednesday.Carillion made an improved offer to Balfour on Tuesday, which represented a 36% premium to the recent average share price, but was rebuffed for a third straight time.Balfour also chose not to extend the 'put up or shut up' deadline which expires at 17:00 on 21 August."Carillion therefore today announces that it is no longer pursuing such a merger," the company said in a statement.Balfour had said earlier that the offer only represented "a small value change" from the previous proposal.The Balfour board again questioned the "considerable risks" around plans to significantly reduce the scale of the UK construction business "when it is poised to benefit from a recovery in the market", and again dug in its heels about its intention to sell its US-based Parsons Brinckerhoff subsidiary.Balfour's share price extended losses after the announcement and was trading down 7.5% at 236.87p by 15:13.BC