In this work we talk about Tanaka’s construction of processes which we can get from a random walk and show that such constructed process is Markov chain. In first chapter we process the necessary theory which is basis for further consideration and that is theory of Markov chain on a countable and general state space. We define terms such as Markov chain, Markov transition function, “forgetfulness” property and stopping times. We show that a random walk is a Markov chain on both a countable and a general state space, and that the time of first entry into the open negative half line for the random walk is the stopping time. Also, we show that Markov chain on countable state space is special case of Markov chain on a general state space. That are just some technical results which are important part of some very important claims which are found in the next chapter. In the second chapter, we construct a new process using Tanaka’s method, which we call the reverse random walk, and which we obtained using some very elementary methods. On a very simple example, we show how reverse random walk is constructed from a random walk, and from this we notice that such a walk has a positive drift. We have defined Markov transition function and proved that it truly is. In the main theorem, we have shown that the reverse random walk is a Markov process on [0; Infinity) with a previously defined Markov transition function, and we have proved this claim in a special case