We have simulated off-lattice 2-dimensional diffusion-limited aggregation (DLA) and have made the growth of the DLA discrete by introducing a discrete time, defined as the time when a new longer branch appears for the first time. From our analysis, we have found that the fractal dimension of DLA can be represented by log 2/log(3/2) = 1.71. This result implies that the contraction rate of 2-dimensional DLA is 2/3. (C) 2002 Elsevier Science B.V. All rights reserved.