This paper presents the searching algorithm to detect a Markovian target which moves
randomly in M-cells. Our algorithm is based on maximizing the discounted effort
reward search. At each fixed number of time intervals, the search effort is a random
variable with a normal distribution. More than minimizing the non-detection
probability of the targets at time interval i, we seek for the optimal distribution of the
search effort by maximizing the discounted effort reward search. We present some
special cases of one Markovian and hidden target. Experimental results for a Markovian,
hidden target are obtained and compared with the cases of applying and without
applying the discounted effort reward search.