Hi Juan,
There is a difference between TRANSPOSE and NOTE SHIFT.

Yamaha uses the word "Transpose" to refer to items that are transmitted by the keyboard and use the term "Note Shift" when referring to the tone generator receiving data,

When you TRANSPOSE the Keyboard +1 Octave, the Key that sends B3 is now one Octave higher. So it follows that if your SPLIT POINT was between B3 and C4 that now moves one Octave higher physically on the Keyboard. That is completely normal.

However, when you know it is the resulting sound that you want to change, this is when you change the synth Tone Generator... which is called "Note Shift". By Note Shifting the tone generator for your left hand and your right hand Part +1 Octave hitting the keyboard you will notice your split point remains physically where it belongs but the sound of the Parts are now Note Shifted up one Octave. B3 when pressed still send B3 Out via MIDI, but the tone generator will sound an Octave higher.

This allows both left hand and right hand Parts to be shifted independently... while leaving the Split Point where it was physically set.
Press [EDIT]
Press [PART SELECT x] to select the Part you wish to edit
Touch "Common" in the lower left of the screen
Touch "Part Settings" > "General"
Find NOTE SHIFT -/+12 = one octave

THANKS BUT I DO NOT REFLECT OCTAVAS, I REFER TO SEMITONOS. WHICH UP OR DOWN FOR SEMITONOS AND THE KEYBOARD IS REMOVED BY THE SAME SITE WHERE I PUT IT ALONE IT RAISES VARIOUS TONES THE SOUNDS DO NOT MOVE. I REPEAT THAT THIS OPTION FOR TRANSPORTATION BY SEMITONO IS MADE BY THE PSR AND TYROS AND THE STRUCTURE OF THE PERFORMANCES IS NOT ALTERED BY MUCH HOW THE SEMITONES BELOW OR UP. IF I LEAVE THE KEYBOARD BY C4 AS IN C4 IS DONE

Works the same for semitones. Just try it.
This is not PSR, note Tyros, this is Montage you can edit the Tone Generator here.
Actually this is similar to how it works in Tyros, sorry, but it's true. In Tyros "Note Shift" is simply referred to as "Tune".
In a Tyros you Transpose the keyboard, you "Tune" the tone generator... on the Mix Console tab "Tune"

But this is Montage, what YOU want is "Note Shift" it works by semitones, 12 equal one Octave. I told you already how to get there.

I think what JUAN said is:
For Example : He Set the G3 for the split point and he's playing the Cm Chord but he is not good with all the Chords in the Cm so he Press Shift Button and Transpose + 3 to play as a Am Chord but Am Transpose + 3 is a Cm...So now his split point will be shift so the G3 is no longer work if he plays some chords at G3

My answer would still be the same. Don't Transpose, use Note Shift!

There's a previous thread where I talk about using superknob to pitch shift in order to avoid having the split point move.

Also in that thread I gave a critique about how tying superknob to all 8 global assignable knobs limited using this as a solution - because if you already have superknob assigned to some other function - in the past, before the 1.50 update - I wished I could "carve out" a global assignable knob to use as the pitch shift master control and leave the superknob assigned to fiddle with the other knobs. Now this is fixed with 1.50 so you can have the cake and eat it with this method.

From 9/16/2016

The problem is once you start using superknob - there's not a way to get an assignable knob detached from superknob. When superknob spins - all 8 assignable knobs will go through their travel between lowest and highest value (even if set to the same value).

I can see that perhaps when you touch the superknob - having the assignable knobs "jump" to a configured fixed single value can have some use - so I would not suggest to make a range of zero (low=some number, high=same number - so range or delta = 0) for an assignable knob. However, it would be nice to somehow make superknob NOT affect an assignable knob.

The use case would be when you want superknob to do something with one set of assignable knobs while using the other "detached" knobs to set values that do not change with the superknob.

There is a different way to skin this cat - use the same assignable knob I am using to control Part 2->Element 1->Volume (which is "All 9 Bars!" 9th drawbar) and only spin that assignable knob rather than superknob. But what if I do want to also use superknob for something? In this case, I'm blocked from using superknob because I have an assignable knob I do not want changing during a performance unless directly spun.

Otherwise - I like everything can have its own curve (even custom). Lots of flexibility except for the "all or nothing" approach to assignable knob movement with superknob.

... it's interesting I got pushback from Yamaha:

This is not a true statement, so conclusions drawn from this will also be faulty.

... however, now the 1.50 firmware implemented a fix to exactly what I was complaining about.

This is the other thread where I talk about superknob for pitch shift (later than above): https://yamahasynth.com/forum/montage-anything-but-lean#reply-12825

... which also again critiques the previous limitation while older firmware tied all 8 global assignable knobs to superknob. So ignore that in today's paradigm.