Dasein's essence is to be open or revealing; the reverse-revealing un- is this unconcealing. So what is proper to Dasein (heimlich) is the reversing-releasing un-; the un- is Dasein's heimlich. It is not that the unheimlich is species of the heimlich, as on Freud's story, but that the power of the un- belongs to the heimlich that it modifies. So the un- that opens Dasein's openness is already a mode of openness.
Further, it is already an uncanny mode of openness. To see this, consider an alternative reading: that what Heidegger is trying to capture with the notion of turning or reversal is what I have called the 'imperfection' of the operation of the un-'s. As we saw, the negating un- does not simply exclude and the reversing-releasing un- does not entirely unconceal. It is such an 'imperfection' that drives Freud's uncanny affect and Heidegger uncanniness. Recall that Dasein's uncanny exclusion from its essence is not a straightforward privation, as if being excluded from openness rendered Dasein not open. Heidegger marks this distinction in HI by contrasting the uncanny human being with the adventurer. The adventurer "remains homeless on account of his lack of rootedness"; he is characterized by a "not being within the homely, a mere departing and breaking free from the homely". The adventurer is not uncanny but "merely not-homely [nicht heimisch]" in the sense of the negating un-. The uncanny human being is not homeless in this way; if anything it is homesick because precisely in being expelled from the home, the human being remains related to it. This persisting relation—that is, the imperfect operation of the un-—seems to be what Heidegger holds is distinctively counter- in out uncanniness.
