For a selfadjoint involution matrix \(J\) on \(\mathbb{C}^{n}\), i.e., \(J=J^{*}\) and \(J^{2}=J\), one can consider \(\mathbb{C}^{n}\) with the indefinite Krein space structure endowed by the indefinite inner product \([x,y]:=y^{*}Jx\). Several authors have studied properties of the Krein space, especially, matrix inequalities based on the indefinite inner product. For two matrices \(A\) and \(B\) satisfying \(A=JA^{*}J\) and \(B=JB^{*}J\), \(A\geq^{J}B\) means that \([Ax,x]\geq [Bx,x]\) for all \(x\in\mathbb{C}^{n}\) if and only if \(JA-JB\) is positive. From the order relation, Löwner-Heinz and Furuta inequalities were derived in [\textit{T.\,Ando}, Linear Algebra Appl.\ 385, 73--80 (2004; Zbl 1059.15025)] and [\textit{T.\,Sano}, Math.\ Inequal.\ Appl.\ 10, No.\,2, 381--387 (2007; Zbl 1141.47014)], respectively. In this paper, the author obtains satellite theorems of the Furuta inequality for the indefinite inner product. Results were already shown for the usual inner product by \textit{E.\,Kamei} in [Math.\ Jap.\ 33, No.\,6, 883--886 (1988; Zbl 0672.47015), Math.\ Jap.\ 49, No.\,~1, 65--71 (1999; Zbl 0934.47009)].