Lidars (Laser radars) are the best suitable instruments to derive the range resolved parameters of atmosphere. Single wavelength and simple backscatter lidars have been widely used to study the height profiles of particle scattering and extinction in the atmosphere. However, atmospheric extinction derived using these lidars data undergo several assumptions and hence involve a significant amount of error in estimation of extinction. The Raman lidar methodology of deriving particle extinction in the atmosphere is a simplified straight-forward method that does not involve any assumptions. The Raman lidar method of atmospheric extinction computation employs derivative of logarithm of normalized range corrected Raman backscattered signal. Usually this causes gaps in the height profiles wherever there is a gradient in the signal under examination. In the present study, a new method is proposed to derive the particle extinction in the atmospheric boundary layer. In this new method, a scheme of alternative solution methodology has been proposed using "Finite Difference Technique". The method has an advantage that, it does not involve the gradient as compared to conventional technique and hence reduces the error. Using this method, the height profiles of particle extinction has been derived. A code in MATLAB is developed to derive the altitude distribution of aerosol extinction. In this connection, the NOAA-REDY site data has been used as the reference data for calculating the molecular extinction in the lower atmosphere.