Experimental design techniques were used to analyze outcomes critically, maximum information with minimal cost, time by avoiding systematic errors and ignoring spurious effects. If the experimental material is homogeneous, partition it into smallest units called “experimental units” such that any unit may receive any treatment (whose effects are to be compared). Most frequently used basic experimental designs for carrying out the analysis are Completely Randomized Design, Randomized Block Design, Latin Square Design, Balanced Incomplete Block Design, etc. To carry out the analysis all the above techniques are based on the assumption of normality. Suppose the responses are measured on nominal or ordinal scale or nature of distribution is unknown, we have to use non-parametric methods for the analysis. They are distributional free, i.e. irrespective of the underlying distribution of the data. Nonparametric method for the analysis of Randomized Block Designs is preferred if the data violates the assumption on normality. When the data is measured on ordinal scale, Kruskal–Wallis and Friedman non-parametric test statistics were used for one way and two way classified data. This paper presents a non-parametric test for the analysis for Randomized Block Design with m-observations per cell.