A task of alternative (faster and more efficient in compression ratio sense) coding of discrete cosine transform (DCT) coefficients within JPEG based image compression approach is considered. In the data processing chain, it is proposed to apply a recursive group coding (RGC) as an alternative to arithmetic or Huffmann coding. In contrast to the aforementioned data coding techniques, the RGC method is able to efficiently code symbols of very large alphabets (each block of 8x8 pixels of quantized DCT coefficients can be represented as such 64-byte or 128-byte symbol). Comparative analysis of efficiency for the standard JPEG and its proposed modification (for three images of three different digital cameras) is carried out using six different quantization tables. It is shown that RCG possesses low computational complexity and a high speed of compression simultaneously with higher compression ratio (CR) compared to the standard JPEG. The benefit in CR appears to be larger for smaller quantization steps (QSs) that mainly correspond to SHQ (super high quality) mode. This benefit can reach up to 10%. It is also demonstrated that the benefits exists for uniform quantization tables. The proposed coding method can be used for an additional compression of JPEG-images in coding traffic of communication lines. For this purpose, data of JPEG-images have to be partly decoded (till the level of the quantized DCT coefficients) and then recoded by RGC.