directivity and beamwidth of antenna

Hi,
I have q question about the relationship between the directivity and the beamwidth:
The higher the directivity of an antenna the wilder the beamwidth ?

Thank you!

Just the opposite, the definition of the directivity: is how much more of the transmitted power goes to certain direction, comparing to isotropic antenna. In other words, if you have a very directive pencil beam antenna, it's beamwidth will be very small...