It is known that for arbitrary transformation monoid $\mathbf{M}$ on a set $A$ the clones $C$ on $A$ with $C^{(1)}=M$ form an interval $Int(M)$ in the clone lattice. The problem is [5]: for which transformation monoids $\mathbf{M}$ on $E_k$, $k>2$, \begin{itemize} ıem[(a)] $Int(M)$ is finite, ıem[(b)] $|Int(M)|=2^{\aleph_0}$? \end{itemize} In this paper we show that there are continuum of clones containing a Picar function [3, Theorem 9, p.\,54] and $|Int(M)|=2^{\aleph_0}$ where $M$ is a given special transformation monoid.