With the wide spread of the discrete wavelet transform, the need for its efficient implementation becomes increasingly important. This work presents an improved version of an algorithm suitable to compute the 2-D discrete wavelet transform on GPU. Depending on the GPU platform, it is suitable to split the 2-D transform computation into separated horizontal and vertical passes. Considering the horizontal passes, we have examined and chosen the best performing method among the already known ones. Furthermore, we have adapted this method for an existing algorithm computing the vertical transform pass. This step helps to reduce several synchronizations and arithmetic operations in the utilized computation scheme. For large data, the proposed vertical method achieves speed-up about 30 % compared to the current state of the art methods. In contrast to previously published works, the presented approach is built on the OpenCL parallel programming framework.