Let A be a nonnegative matrix of size n x n. A is said to be nearly convertible if A(i｜j) is convertible for all integers i, j ∈ {1, 2, …, n} where A(i｜j) denote the submatrix obtained from A by deleting the i-th row and the j-th column. We investigate some properties of nearly convertible matrices and existence of (maximal) nearly convertible matrices of size n is proved for any integers n(≥ 3).