Does the toolbox have biorthogonal coiflets?

Hello,

I have read some information on coiflet wavelets provided by the following command:

waveinfo('coif');

It says coiflets could be both orthogonal and biorthogonal, and this makes me confused a lot. There are some papers on the web talking about biorthogonal coiflets, but I do not understand whether those are implemented in the toolbox. By typing in something like

[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('coif1'),

I can clearly see that the same filter coefficients are used for both analysis and synthesis, and these vectors are apparently orthogonal (if properly shifting either of the two). That is not the case for 'bior2.2.', for example, where we have two different sets of vectors for analysis and synthesis.

Summing up, I do not seem to understand what is "biorthogonal" about the coiflets implemented in the toolbox.

Please help me figure this out. Thanks in advance.