jointly gaussian

Can somebody please help me with this question:

can a bivariate normal distribution be only made up of 2 random
variables with normal distribution (and independent of each other)? In
other words can two random variables with some distribution other than
normal give rise to a jointly normal distribution?

Or is it just that for 2 normal variables to have a jointly normal
distribution, they need to be independent of aech other?

- thanks,
b

.