We present a new method developed for measuring radiocarbon of methane (14CH4) in ancient air samples extracted from glacial ice and dating 11,000–15,000 calendar years before present. The small size (∼20 μg CH4 carbon), low CH4 concentrations ([CH4], 400–800 parts per billion [ppb]), high carbon monoxide concentrations ([CO]), and low 14C activity of the samples created unusually high risks of contamination by extraneous carbon. Up to 2500 ppb CO in the air samples was quantitatively removed using the Sofnocat reagent. 14C procedural blanks were greatly reduced through the construction of a new CH4 conversion line utilizing platinized quartz wool for CH4 combustion and the use of an ultra-high-purity iron catalyst for graphitization. The amount and 14C activity of extraneous carbon added in the new CH4 conversion line were determined to be 0.23 ± 0.16 μg and 23.57 ± 16.22 pMC, respectively. The amount of modern (100 pMC) carbon added during the graphitization step has been reduced to 0.03 μg. The overall procedural blank for all stages of sample handling was 0.75 ± 0.38 pMC for ∼20-μg, 14C-free air samples with [CH4] of 500 ppb. Duration of the graphitization reactions for small (<25 μg C) samples was greatly reduced and reaction yields improved through more efficient water vapor trapping and the use of a new iron catalyst with higher surface area. 14C corrections for each step of sample handling have been determined. The resulting overall 14CH4 uncertainties for the ancient air samples are ∼1.0 pMC.