It seems to me that Heidegger was trying to formulate Being in other terms than those of Being. For instance, in Being and Time, he says:
“Das Sein des Seienden “ist” nicht selbst ein Seiendes.”
[section 2.]
Translation:
“The Being of that which is “is” not itself something that is.”
This may become intelligible when we replace all forms of the verb “to be” in this sentence (except the one between quotation marks) by the corresponding forms of the verb “to run”:
“The running of that which runs is not itself something that runs.”
So what is this Being of that which is, if not itself something that is? - Again, I will quote from section 2, this time the beginning of the next paragraph:
“Sofern das Sein das Gefragte ausmacht, und Sein besagt Sein von Seiendem, ergibt sich als das Befragte der Seinsfrage das Seiende selbst.”
Translation:
“In so far as Being is the object of our inquiry - and “Being” means Being of that which is -, that which is proves to be itself the object of our inquiry after Being.”
This is because the Being of that which is is not itself something that is. So the Being of that which is has itself no Being. Only that which is has Being, and it is this Being that is the object of our inquiry. Therefore, as that which is, is [i.e., has Being], the object of our inquiry is that which is itself: it is this that we shall endeavour to understand.