This study proposes a Coding Tree Assignment Scheme with Improved Search-Order Coding algorithms (CTAS-ISOC) to enhance the coding efficiency of the original SOC by exploiting the correlations of the neighbouring blocks using the left-pair and upper-pair patterns in the index domain. The essential techniques consist of three major elements: the Neighbouring Index Code Assignment (NICA), the Left-pair Search-Order Coding (LSOC) and the Upper-pair Search-Order Coding (USOC). The NICA approach assigns a short code to the current index by using the statistics on the indices of the neighbouring blocks. The LSOC (USOC) compares the current left (upper) index pair with previous index pairs in a predefined search path. Since the predefined search path is exploited with a correlation viewpoint, both LSOC and USOC achieve better compression than the original SOC. Experimental results demonstrate the effectiveness of the proposed scheme in comparison with some existing popular lossless index coding schemes.