In this paper, there have analyzed three problems occurred in the incomplete Cholesky factorization with thresholds for the matrices of symmetric positive definite. First, the drop strategy is used to only a row of the matrix at a time. Based on the idea of dropping the small elements in magnitude, this strategy is extended, that is, several rows of the factor are computed and the drop strategy is exploited for these rows at a time. Second, there may occur pivots of small magnitude or even negative ones. A solution is proposed in this paper. Finally, the incomplete factorization is often difficult to implement efficiently. Several integer vectors are exploited in this paper to solve this problem. Then the efficient implementation of the modified incomplete Cholesky decomposition is in consideration. Analyses and computation experiments show that these techniques are effective.