This paper describes the validation of a new background discrimination method based on Random Forest technique by re-analysing the Markarian 421 ( Mrk 421 ) observations performed by the TACTIC ( TeV Atmospheric Cherenkov Telescope with Imaging Camera ) \gamma -ray telescope . The Random Forest technique is a flexible multivariate method which combines Bagging and Random Split Selection to construct a large collection of decision trees and then combines them to construct a common classifier . Markarian 421 in a high state was observed by TACTIC during December 07 , 2005 - April 30 , 2006 for 202 h. Previous analysis of this data led to a detection of flaring activity from the source at Energy > 1 TeV . Within this data set , a spell of 97 h revealed strong detection of a \gamma -ray signal with daily flux of > 1 Crab unit on several days . Here we re-analyze this spell as well as the data from the entire observation period with the Random Forest method . Application of this method led to an improvement in the signal detection strength by \sim 26 \% along with a \sim 18 \% increase in detected \gamma rays compared to the conventional Dynamic Supercuts method . The resultant differential spectrum obtained is represented by a power law with an exponential cut off \Gamma = -2.51 \pm 0.10 and E _ { 0 } = 4.71 \pm 2.20 TeV . Such a spectrum is consistent with previously reported results and justifies the use of Random Forest method for analyzing data from atmospheric Cherenkov telescopes .