The paper is concerned with the construction of \(K\)-frames proposed by \textit{L. Găvruţa} [Appl. Comput. Harmon. Anal. 32, No. 1, 139--144 (2012; Zbl 1230.42038)], where \(K\) is a bounded linear operator on a separable Hilbert space \(H\). Bounded linear operators on \(l^{2}\) that transform a pair of Bessel sequences into \(K\)-frame have been characterized. Also, a sufficient condition to obtain \(K\)-frame from two orthogonal (disjoint) \(K\)-frames has been presented. Finally, Parseval \(K\)-frames and \(K\)-frames with prescribed norms of the vectors when \(\dim (H)<\infty\), have been investigated. In the last some examples also have been provided to illustrate the generality of the frame theory.