  We present an Oppenheim type determinantal inequality for positive definite
block matrices. Recently, Lin [Linear Algebra Appl. 452 (2014) 1--6] proved a
remarkable extension of Oppenheim type inequality for block matrices, which
solved a conjecture of G\"{u}nther and Klotz. There is a requirement that two
matrices commute in Lin's result. The motivation of this paper is to obtain
another natural and general extension of Oppenheim type inequality for block
matrices to get rid of the requirement that two matrices commute.
