Computer-simulation techniques are used to study the domain-growth kinetics of (2×1) ordering in a two-dimensional Ising model with nonconserved order parameter and with variable ratio " of next-nearest- and nearest-neighbor interactions. At zero temperature, persistent growth characterized by the classical growth exponent n 12 is found for " 1, whereas the domain boundaries become pinned and the growth stops for "<1. For finite temperatures and " 1, the growth exponent is found to be temperature independent in a wide regime, and for "1 the domain walls unpin and growth resumes.