A hidden Markov model (HMM) is a statistical tool applied to model stochastic sequences. In an ordinary HMM a hidden Markov chain named, the chain of states emits a sequence of observations. In this model, given a state the emissions are assumed to be independent from each other. However several researchers have already studied the dependencies between emissions. In this paper a new approach for consideration of dependencies among emissions is presented. We start with the use of the information of the left hand side of any emission and introduce a new model. We then take the information of the right hand side of any emission into account. Protein is one of the most important molecules in any living cells and the study of protein structure is very important in biology. Predicting the secondary structure of a protein is usually used for the 3D structure prediction of it which in turn helps to identify a protein structure in whole. In this paper we discuss a two-sided modified HMM considering some dependencies among emissions. This model construction seems to be reasonable and improves the precision of protein secondary structure prediction.