A method for estimating the extent of denitrification of Arctic polar vortex air is proposed. Previous estimates of denitrification using tracer-tracer scatter plots have not allowed for mixing-induced changes in tracer-tracer relationships in a sufficiently general way. This difficulty is overcome by constructing an artificial reference tracer from a linear combination of other long-lived tracers. The reference tracer is designed so that, as far as possible, it has a linear canonical relationship with NOy in midlatitudes. A linear relationship is unaffected by mixing, so denitrification is apparent as deviations of vortex measurements from the linear midlatitude relationship. The method is first demonstrated using data from a chemical transport model in which no denitrification processes are present. It is then applied to balloon, aircraft and shuttle-borne measurements made before and during the breakdown of the Arctic vortex in 1992--1993 and 1996--1997. In each case the method indicates that little or no denitrification had occurred in any of the vortex air encountered. When the method is applied to the southern hemisphere vortex in 1994, by contrast, denitrified air is clearly seen to be present around 19--23 km in the vortex.