Let \(L\) be a mean value (continuous, symmetric, between max and min) on an open real interval \(I\). The author defines \[ L_{\varphi}(x,y)=\varphi^{-1}(\varphi(x)+\varphi(y)-\varphi[L(x,y)]), \] where \(\varphi\) is a continuous real valued function on \(I\). He offers, among others, necessary and sufficient conditions for equality and comparison (which is greater on \(I^{2}\)) of such means, for their homogeneity (if \(L\) is homogeneous) and for the similar translativity property (where addition takes the place of multiplication). A necessary and sufficient condition for \(A_{\varphi}\) to be a quasiarithmetic mean (a conjugate of the arithmetic mean \(A\)) is offered for twice differentiable strictly monotonic \(\varphi\), cf. \textit{J. Matkowski} [Aequationes Math. 57, No.1, 87-107 (1999; Zbl 0930.26014)].