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The discrete Tchebichef transform (DTT) is a transform method based on discrete orthogonal Tchebichef polynomials, which have applications recently found in image analysis and compression. This letter introduces a new fast 4 x 4 forward DTT algorithm. The new algorithm requires only 32 multiplications and 66 additions, while the best-known method using two properties of the DTT requires 64 multiplications and 96 additions. The proposed method could be used as the base case for recursive computation of transform coefficients. Experimental results showing performance improvement over existing techniques are presented.