  The burning number conjecture states that the burning number of a connected
graph is at most $\lceil \sqrt{n} \rceil.$ While the conjecture is unresolved,
Land and Lu proved that the burning number of a connected graph is at most $
\sqrt{(3/2)n}+O(1).$ Using an algorithmic approach, we provide an improved
upper bound for the burning number of a connected graph: $$\bigg \lceil
\frac{\sqrt{12n+64}+8}{3} \bigg \rceil = \sqrt{(4/3)n} +O(1) .$$
