Discrete Cosine Transform (DCT) is widely used transform in many areas of the current information age. It is used in signal compression such as voice recognition, shape recognition and also in FBI finger prints. DCT is the standard compression system used in JPEG format. The DCT quality deteriorates at low-bit compression rate. The deterioration is due to the blocking artifact inherent in block DCT. One of the successful attempts to reduce these blocking artifacts was conversion of Block-DCT into Line-DCT. In this thesis we will explore the Line-DCT and introduce a new form of line-DCT called Bidirectional-DCT, which retains the properties of Line- DCT while improving computational efficiency. The results obtained in this thesis show significant reduction in processing time both in one dimensional and two dimensional DCT in comparison with the traditional Block-DCT. The quality analysis also shows that the least mean square error is considerably lower than the traditional Block-DCT which is a consequence of removing the blocking artifacts. Finally, unlike the traditional block DCT, the Bidirectional-DCT enables compression with very low bit rates and very low blocking artifacts.