Can something be both new and improved?

Just found this grammar blog:
Imagine, if you will, that I am a purveyor of tasty snacks. Tasty as they are, I decide to improve the recipe with which my snacks are created. When I sit down to design the packaging I decide to put the phrase "NEW, IMPROVED RECIPE!" all over it.

Aside from the glaring error of using capitalised type, I find myself with another quandary: can my recipe be both new and improved at the same time?