In this paper, we derive new split-radix DCT-algorithms of radix-2 length, which are based on real factorization of the corresponding cosine matrices into products of sparse, orthogonal matrices. These algorithms use only permutations, scaling with $sqrt{2}$, butterfly operations, and plane rotations/rotation-reflections. They can be seen by analogy with the well-known split-radix FFT. Our new algorithms have a very low arithmetical complexity which compares with the best known fast DCT-algorithms. Further, a detailed analysis of the roundoff errors for the new split-radix DCT--algorithm shows its excellent numerical stability which outperforms the real fast DCT-algorithms based on polynomial arithmetic.