# Do Karnaugh maps yield the simplest solution possible?

I'm learning to use a Karnaugh map, but I'm not sure if I obtained the simplest expression possible. Have a look at this example:

Truth table (inputs are A B C; output is F):

A   B   C   |   F
0   0   0   |   1
0   0   1   |   0
0   1   0   |   1
1   0   0   |   0
0   1   1   |   1
1   0   1   |   1
1   1   0   |   0
1   1   1   |   1


The Karnaugh map looks like this:

AB
--
C|

00  01  11  10
--------------
0|  (1  1)  0   (1)
1|  0   (1  1)  (1)


And this yields $\bar{C}\bar{A}+CB+A\bar{B}$. Is there any simpler way of choosing the 1s from the map and getting a simpler result? Are Karnaugh maps guaranteed to always yield the simplest result possible?