not really maybe another 2 inches
No, but it is just right for me, I am 5' 8" and about 210lbs. The absolutely easiest mower to push.
My Murray 22 inch High Wheel mower ($168) came with the economy 2 position handle, which is 39-1/4 high at the top of the handle. It can be adjusted (by removing 3 bolts and two cotter spring clips) to a lower position, 38-1/2 inches at the handle top. Not a big change, but some help.
Murray also has 2 models of 3 position handles, EZ and QUICK, which I assume come on higher price models. How to adjust them (all 3 models) is in my owners instruction manual.
This model has a high and a low setting, which are very easy to position the handle. I am 5'10", and did not need to adjust the handle. It could be adjusted lower.