The author obtains an explicit solution formula for the tetrachoric homogeneous difference equation \[ u_{n + p} = a_r(n) u_{n + r} + a_1(n) u_{n + 1} + a_0(n) u_n, \] with \(u_i = c_i\) \((i = 0, 1, \dots, p - 1)\), where \(n \in \mathbb{N}_0 : = \{0,1,2, \dots\}; p\) and \(q\) are natural numbers with \(p > r\); \(c_0, \dots, c_{p - 1}\) are real numbers, and \(a_0, a_1, a_r : \mathbb{N}_0 \to \mathbb{R}\) are given functions. By induction, the author gives the solution formula of above difference equation in the form \[ u_{n + p} = \sum^2_{i = 0} \sum^{p - 1}_{j = s_i} \biggl\{ \bigl[ F(n - j + s_i, n) \bigr] c_j \biggr\} a_{s_i} (j - s_i), \quad n \in \mathbb{N}_0 \] where \(s_0 = 0\), \(s_1 = 1\), \(s_2 = r\), and the function \(F : \mathbb{N}^2_0 \to \mathbb{R}\) is defined in the paper by a very long expression. It is also indicated that, if \(a_k (n) = a_k =\) constant, for \(k = 0,1,r\), then the last solution formula reduces to \[ u_{n + p} = \sum^2_{i = 0} \left\{ \sum^{p - 1}_{j = s_i} \bigl( c_j f(n - j + s_i) \bigr) a_i \right\}, \quad n \in \mathbb{N}_0, \] with \(f(m) = \sum {(b_0 + b_1 + b_r) \over b_0! b_1! b_r!} a_0^{b_0} a_1^{b_1} a_2^{b_r}\), where the summation is performed over all nonnegative integer solutions of the following Diophantine equation \[ pb_0 + (p - 1) b_1 + (p - r) b_r = m. \]