change level of positive square wave signal to negative
You apparently want to drive a transformer primary with a 5 V square wave, and what you have goes from 0 V to 5 V.

First, check whether this is even a problem at all.  How much current will the transformer draw with 2.5 V DC input?  Would 5 V DC input saturate the core or not.  If the average DC current is acceptable and the core won't saturate, then you don't need to do anything.

Otherwise, put a capacitor in series.

However, you have bigger problems since you don't seem to understand transformers and you specs don't make sense:

My transformer is a 1:0.8 (primary:secondary) and the voltage on the secondary side that I need, is about 10-12 volts

This won't work.  With a 5 V square wave in and a 1 to 0.8 ratio, you will get a 4 V square wave out.

I you want 10 V out, you need a transformer with more than 1:2 ratio.  1:2 will give you 10 V out unloaded.  You need a bit more to compensate for the loss in the transformer, and the diode drop in rectifying the output.

Overall, you need to step back and figure out what you really want.  Your question makes no sense as currently written.