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In this paper, we continue the study of cominimaxness modules with respect toan ideal of a commutative Noetherian ring (cf. \cite{ANV}), and  Bass numbers of local cohomology modules.  Let $R$ denote a commutative Noetherian local ring and $I$ an ideal of $R$.We first show that the Bass numbers $\mu^0(\frak p, H^2_I(R))$ and $\mu^1(\frakp, H^2_I(R))$ are finite for all $\frak p\in \Spec R$, whenever $R$ is regular.As a consequence, it follows that the Goldie dimension of $H^2_I(R)$ is finite.Also, for a finitely generated $R$-module $M$ of dimension $d$, it is shownthat the Bass numbers of $H^{d-1}_{I}(M)$ are finite if and only if$\Ext^i_R(R/I, H^{d-1}_{I}(M))$ be minimax for all $i\geq0$. Finally, we provethat if $\dim R/I=2$, then the Bass numbers of $H^{n}_{I}(M)$ are finite if andonly if $\Ext^i_R(R/I, H^{n}_{I}(M))$ be minimax, for all $i\geq0$, where $n$is a non-negative integer.

On the finiteness of Bass numbers of local cohomology modules and Cominimaxness