angular momentum - Possible inconsistency in Bohr atom model

It is well known that Bohr model is not totally right. But I recently discovered a very curious inconsistency (if I am right) which I haven't seen explained anywhere.

The first postulate of Bohr theory is that the Orbital momentum of the electron is quantized $L = mvr=nh$ (where $h$ mean the Dirac constant). This means that if there is a transition between level $n=5$ to $n=1$ (Balmer series) the orbital momentum changes by $4h$!!! Based on this rule and his second postulate Bohr finds the right energy for this transition (and all others as well). But this transition is a release of just one photon and a photon has spin $1h$. $(h,0,-h)$. So it can change the orbital momentum with $1,0$ or $-1$ and not by $4$. Maybe the spin of electron can also change with $1$ (from $\frac{1}{2}$ to -$\frac{1}{2}$) which combined changes orbital momentum by most 2. I'm very surprised to make such conclusion.

I am wrong here?