In the paper we continue to investigate measures of dependence for random variables with infinite variance. The asymptotic of spectral covariance $ρ(X_{(0,0)}, X_{(k_1,k_2)})$ for linear random field $X_{k,l}=\sum_{i,j=0}^\infty c_{i,j}ε_{k-i, l-j}, \ (k, l)\in \mathbb{Z}^2,$ with special form of filter $\{c_{i,j}\}$ and with innovations $\{ ε_{i, j}\}$ having infinite second moment is investigated. Different behavior of $ρ(X_{(0,0)}, X_{(k_1,k_2)})$ is obtained in the cases $n\to \infty, \ m\to \infty$ and $n\to \infty, \ m\to -\infty$, the latter case being much more complicated.