This paper considers multifunctions on two-elements set  with superposition defined in a special way. Set of all multifunctions contains set of Boolean functions, set of partial functions and set of hyperfunctions. Clone of multifunctions is a set closed under superposition. Interval I (A, B) is a partially ordered by inclusion set of all subclones of B containing A.
This paper describes a fragment of an interval in the lattice of clones containing all multifunctions preserving 0 and 1 (if particular function simultaneously preserves 0 and 1 then it cannot have an empty set as a value on any input). It is known that interval of partial Boolean functions preserving 0 and 1 consists of 45 clones.
This paper shows that considered interval contains 12 clones and has an isomorphic interval in the lattice of clones of partial functions.

1. Alekseev V.B. On Some Closed Sets in Partial Two-Valued Logic. Disktretnaya matematika, 1994, vol. 6, no. 4, pp. 58-79.

2. Zhuk D. A Structure of Closed Sets in a Maximal Set of Self-Dual Functions of Three-Valued Logic. Dokl. Ros. Akad. Nauk, 2011, vol. 437, no. 6, pp. 738-742.

3. Panteleyev V.I. Completeness Criterion for Incompletely Defined Boolean Functions. Vestnik Samar. Gos. Univ. Est.-Naush. Ser., 2009, vol. 2, no. 68, pp. 60-79.

4. Panteleyev V.I. On Two Maximal Multiclones and Partial Ultraclones. Izvestiya Irk. Gos. Univ. Ser. Matematika, 2012, vol. 5, no. 4, pp. 46-53.

5. Lau D. Function Algebras on Finite Sets. A Basic Course on Many-Valued Logic and Clone Theory. Berlin, Springer-Verlag, 2006. 668 p.

6. Doroslovacki R., Pantovicj., Vojvodic G. One Interval in the Lattice of Partial Hyperclones. Chechoslovak Mathematical Journal, 2005, no. 55(130), pp. 719-724.

7. Pantovic J., Vojvodic G. On the Partial Hyperclone lattice. Proceedings of 35th IEEE International Symposium on Multiple-Valued Logic [ISMVL 2005], 2005, pp. 96-100.

8. Post E. L. Two-valued iterative systems of mathematical logic. Annals of Math. Studies, Princeton, Univ. Press, 1941, vol. 5. 122 p.