Summary: Let \(I\) be a \(2 \times 2\) identity matrix, and \(M\) be a \(2\times 2\) dilation matrix with \(M^2 = 2I\). First, we present the correlation of the scaling functions with dilation matrix \(M\) and \(2I\). Then by relating the properties of scaling functions with dilation matrix \(2I\) to the properties of scaling functions with dilation matrix \(M\), we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix \(M\). Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.