Discrete cosine transform (DCT) has wide applications in speech and image coding. In this paper, we propose a novel fast dCT scheme with the property of reduced multiplication stages and the smaller number of additions and multiplications. This exploits the symmetry property of the DCT kernel to decompose the N-point dCT to N/2 point, and can be generally applied recursively to $2^{m}$-point. The proposed algorithm has a structure that most of multiplications tend to be performed at final stage, and this reduces propagation of truncation error which could occur in the fixed-point computation. Also the minimization of the multiplication stages further decreases the error.