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The necessity of recognizing handwritten characters is increasing day by day because of its various applications. The objective of this paper is to provide a sophisticated, effective and efficient way to recognize and classify Bangla handwritten characters. Here an extended convolutional neural network (CNN) model has been proposed to recognize Bangla handwritten characters. Our CNN model is tested on "BanglalLekha-Isolated" dataset where there are 10 classes for digits, 11 classes for vowels and 39 classes for consonants. Our model shows accuracy of recognition as: 99.50% for Bangla digits, 93.18% for vowels, 90.00% for consonants and 92.25% for combined classes.