The bidispersive equation, accounting for second-order temporal dispersion in a lossless medium, is examined under a Galilei-like transformation, as well as a conditional ordinary Galilei transformation. In the former case, the roles of space and time are reversed by comparison to the application of the same transformation to the quantum mechanical Schrödinger equation. Such an invariance can result in envelope speeds that can assume values above or below the group speed of the medium; also, they can be negative. Conditional Galilei transformation results in a decrease in dimensionality.