We are interested in the conditional independence in sparse $2 ims2 ims$K tables with very rare cell counts. The most popular test is Cochran-Mantel-Haenszel statistic when sample sizes are moderately large enough to guarantee the chi-square approximation. We will consider jackknifing the CMH test and also suggest an approximate normal distribution for the standardized jackknifed CMH statistic. The main focus of this paper is to improve the chi-squared approximation to the CMH test by using the asymptotic normality of the jackknifed CMH test when sample sizes are very sparse but K and N$infty$. The performance of the proposed jackknifed test, in the sense of significance level control and power, will be compared with that of the CMH test through a Monte Carlo study.