We give an alternate description of Koiter's shell equation that does not depend on the special mid surface coordinates, but uses differential operators defined on the mid surface. This is the continuation of the preprint CSC12-02 (http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-96903) due to new additional simplifications of these operators.:1. Introduction 2. Basic differential geometry 3. The strain tensor and its simplifications 4. Linearization to small strain and coordinate free description 5. The resulting Koiter energy 6. Remarks on the differential operators