Summary: Burning number is a discrete graph algorithm parameter inspired by the spread of social contagion. A. Bonato et al. [Internet Math. 12, No. 1–2, 85–100 (2016; Zbl 1461.05193)] that for any connected graph of order \(N^2\), the burning number is at most \(N\). In this work, we prove that an earlier slightly strengthened burning number conjecture holds for trees with sufficiently long arms.