<p>Due to their potential applications in video images, color images, and multi-spectral images, matrix-valued frames have attracted the attention of scholars from mathematics and engineering communities. A Hilbert–Schmidt frame (HS-frame) can be considered to be square matrix-valued. In this paper, we introduce the concepts of generalized Hilbert–Schmidt frame (GHS-frame) and oblique dual GHS-frame (ODGHS-frame). The former is more general than HS-frame and includes general matrix-valued frames (not necessarily square matrix-valued frames) as a special case. We give a parametric expression of all ODGHS-frames of an arbitrarily given GHS-frame, and prove that the portraits of a given ODGHS-frame pair (GHS-orthonormal basis, dual GHS-frame pair) under suitable bounded operators give other ODGHS-frame pairs. Finally, as an application of the above results, we derive an existing result and some new results on usual frames.</p>