Calling All Engineers! All Math Teachers! All Smarty Pants!!

Okay, so my hubby and I need some help with a brain teaser, of sorts. We are trying to create a rotation schedule. But, for the life of us (and some others, who's assistance we've summoned), we can't get it right. It seems like it should be fairly simple. But, it is not!
Here's the situation: We have 12 couples participating. Each couple is to meet with every other couple, once. This means that each month each couple will be meeting with a different couple (one with whom they have not yet met) to get to know them better. So, twelve couples=11 total meetings (because there are 11 couples besides yourself to meet with). We will meet January through November with a different couple.

We have assigned each couple a number and tried to pair up the numbers, so that each month, different "numbers" meet with different "numbers" than they have before. But, each time we get close, there is a duplicate. Some couple ends up being paired up to meet with a couple they've already met with previously in the year. Some people have tried to pair them up like the table I pasted at the bottom of this blog. But, this table doesn't work... because, as you can see, Couple #1 is paired with Couple #2 for January. But, Couple Number 2 is paired with Couple #3 for January. Couple #2 can't be paired with two different couples in one month. So, if anyone loves a challenge, I have one here for you. Figure out how to have all 12 couples meet with every other couple, but only once. The first person to provide an accurate answer or to provide a spreadsheet with a rotation that works will win a prize! I promise! We are that bewildered by this scheduling problem. :) Thanks!