The wavelet transform is robust analysis tool in the field of signal processing and image processing. Especially. in the field of image compression such as JPEG2000 and MPEG4, wavelet transform has a main roles for transform coding. This paper represents essentially wavelet transform algorithm using lifting and dual lifting scheme proposed by I. Daubieches and W. Sweldens. In this paper We detailedly derive their achievement for its algorithm. As a result the procedure of wavelet transform algorithm using lifting and dual lifting scheme is analyzed and derived.