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Several applied linear algebra research areas, such as eigenvalue localizations, infinity norm estimations for matrix inverse, pseudospectra localizations, etc., are closely connected with special subclasses of nonsingular H-matrices. Many of them have already been investigated in details, but it seems that finding new such subclasses is far from completed. For example, in [22], interchanging the quantifiers in the definition of the Dashnic-Zusmanovich matrices, led to a new class, benefits of which was shown in [22], [13], [11]. In this paper we will apply similar idea to CKV class (also known in the literature under the name Σ-SDD class), and show several benefits from the obtained new class, which we will call CKV-type matrices. © 2020 Elsevier Inc.