Pierre,
If you don't remove that 'old' balun, then you don't have a 4:1
conversion anymore, but with 'both' baluns connected, it's more on the
order of an 8:1 conversion. Is that 'bad'? That depends on the
antenna's impedance and the feed line's impedance, but in general, I
would think that it wouldn't exactly be the 'best' thing you could
do. Removing the 'old' balun would probably be your 'best' bet. May
make making connections a little more difficult (or at least
'different') but still the 'best' solution.
Then again, before doing that "out with the old" thingy, try it and
see what the results are with both baluns in-line. Results 'better'
with or without the old balun still in line? Hmm, if I had to
'guess', I'd have to say removing the old balun would probably be your
best bet. At the very least, it means a little less weight hanging on
the antenna, one less 'point of loss' in the whole thing...
- 'Doc

(May not be the 'best' answer in the world, but it's sure a nice
"CYA"... ain't it?)