This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic Cp-Whitney fields (with p finite). In this new version we consider Whitney fields definable in an arbitrary o-minimal structure on any real closed field R and obtain an extension which is a Cp-function definable in the same o-minimal structure. The Whitney fields that we consider are defined on any locally closed definable subset of Rn. In such a way, a local version of the theorem is included.