The hidden Markov chain (HMC) model is a couple of random sequences (X,Y), in which X is an unobservable Markov chain, and Y is its observable ''noisy version''. The chain X is a Markov one and the components of Y are independent conditionally on X. Such a model can be extended in two directions: (i) X is a semi-Markov chain and (ii) the distribution of Y conditionally on X is a ''long dependence'' one. Until now these two extensions have been considered separately and the contribution of this paper is to consider them simultaneously. A new ''semi-Markov chain hidden with long dependence noise'' model is proposed and it is specified how it can be used to recover X from Y in an unsupervised manner. In addition, a new family of semi-Markov chains is proposed. Its advantages with respect to the classical formulations are the low computer time needed to perform different classical computations and the facility of its parameter estimation. Some experiments showing the interest of this new semi-Markov chain hidden with long dependence noise are also provided