This paper presents a new measure of core inflation for the UK based on the idea that it is the persistence of individual inflation rates which matters in measuring the level of underlying inflation. The measure is based on the same components as RPIX, but it weights individual price changes by their past persistence, instead of their importance in households' budgets, to derive a persistence-weighted core inflation measure, or RPIXP for short. This operationalises Blinder's concept of core inflation as the durable or persistence part of aggregate inflation. The paper evaluates this new measure against existing measures in terms of its ability to predict future RPIX inflation. It finds that the new RPIXP is a good predictor of RPIX 6 months and 12 months ahead, and outperforms most other core inflation measures, as well as current RPIX itself, in its predictive ability. Surprisingly, RPIX excluding food and energy - which is a popular way of measuring underlying inflation - is a poor predictor of RPIX. One reason is that this measure excludes non-seasonal food prices which are highly persistent in the UK.