Progressive wavelet coding of Images (PWC) is a simple and efficient image coding algorithm. It is comparable to the state-of-the-art SPIHT. It is based only on two concepts: (1) data-independent reordering and blocking, and (2) low-complexity independent encoding of each block via adaptive run-length/Rice coding of the bit planes. Therefore PWC allows for progressive image encoding that is scalable both in resolution and bit rate. But its reordering and un-reordering algorithms are very complex and computation speed is limited, so this paper proposes a new reordering and un-reordering algorithm to improve significantly the encoding and decoding speed of PWC, making PWC have wide applications.