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A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. In this paper, a new infinite family of tetravalent half-arc-transitive graphs with girth 4 is constructed, each of which has order 16m such that m > 1 is a divisor of 2t 2 + 2t + 1 for a positive integer t and is tightly attached with attachment number 4m. The smallest graph in the family has order 80.doi:10.1016/j.disc.2006.05.009 fatcat:ahywc7te6bgl3a4iw7o5e7uchm