In this paper, a high accuracy and reduced processing time block based classification method for computer screen images is presented. This method classifies blocks into five types: smooth, sparse, fuzzy, text and picture blocks. In a computer screen compression application, the choice of block compression algorithm is made based on these block types. The classification method presented has four novel features. The first novel feature is a combination of Discrete Wavelet Transform (DWT) and colour counting classification methods. Both of these methods have only been used for computer image compression in isolation in previous publications but this paper shows that combined together more accurate results are obtained overall. The second novel feature is the classification of the image blocks into five block types. The addition of the fuzzy and sparse block types make the use of optimum compression methods possible for these blocks. The third novel feature is block type prediction. The prediction algorithm is applied to a current block when the blocks on the top and the left of the current block are text blocks or smooth blocks. This new algorithm is designed to exploit the correlation of adjacent blocks and reduces the overall classification processing time by 33%. The fourth novel feature is down sampling of the pixels in each block which reduces the classification processing time by 62%. When both block prediction and down sampling are enabled, the classification time is reduced by 74% overall. The overall classification accuracy is 98.46%.