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We introduce the new class of continua; $D^{**}$-$continua$. The classes ofWilder continua and $D^{*}$-continua are strictly contained in the class of$D^{**}$-continua. Also, the class of $D$-continua is bigger than the class of$D^{**}$-continua. Using $D^{**}$-continua, we give the negative answer to aQuestion. Furthermore, we prove that being Wilder, being $D$, being $D^*$ andbeing $D^{**}$ are Whitney properties.

Some decomposable continua and Whitney levels of their hyperspaces