<p><b>Abstract</b>—This paper establishes the exact upper bound for Lawler's heuristic proving that its schedule of a UECT tree on <it>m</it> identical processors does not exceed an optimal solution by more than <tmath>${m \mathord{\left/ {\vphantom {m 2}} \right. \kern-\nulldelimiterspace} 2}$</tmath> time units.</p>