Howard Mather Burnham (March 17, 1842 – September 19, 1863), was a Union Army artillery officer in the American Civil War who was killed in action at the Battle of Chickamauga.

[4] In April 1863, Burnham was promoted to first lieutenant and joined the Battery H, 5th U.S, Artillery of the Army of the Cumberland under General William Rosecrans.

[5] Following the departure of First Lieutenant Francis Guenther (promoted), as senior lieutenant present, Burnham assumed command in August 1863 in absence of the battery's captain (George A. Kensel); shortly after assuming command of Battery H, as the senior Regular Army artillery officer in the division, he was appointed Chief of Artillery of the 1st Division, XIV Corps, on the staff of Gen. Absalom Baird.

[2] On the morning of September 19, 1863, Burnham was directing his artillery battery in the thick woods near Jay's Mill at the Battle of Chickamauga.

[4] When sole remaining battery officer Second Lieutenant Joshua A. Fessenden asked Burnham if he was hurt, he responded: "Not much, but save the guns!".

[6] Battery H was overrun, but Fessenden successfully rallied his troops, recaptured his artillery pieces, and even captured one Confederate gun.

Gen. John King dispatched the following in his report: I take this occasion to speak in the highest terms of the officers of Battery H, 5th Artillery, 1st Lieut.