Recently, Schwartz and Etzion proposed several efficient code construction methods of two-dimensional linear codes capable of correcting a single arbitrary cluster of errors of size . Some of their methods, however, impose the constraint that the degree of GF must be even. In this correspondence, we investigate whether such Schwartz-Etzion's methods are applicable to the case is odd. We provide necessary and sufficient conditions for the original Schwartz-Etzion's methods to be used for constructing two-dimensional cluster-error-correcting linear codes for odd , and show that the methods are available extensively.