Generating random correlated numbers

I am creating x vectors of random numbers, each of them using

for i=1:x
  A(i,:) = randperm(n)
end

So one of the outcomes could be

   1 2 3 5 4 7 6 ... n

But obviously, each vector that I create is independent of the others. I would like to create random vectors that are correlated, i.e. that if 1 appears before 2 in the previous vector, it also has a high chance to be before 2 in the next vector.

Each number needs to appear once and only once on each vector. Any ideas would be appreciated.

[Mark Matusevich]

It is unclear what distribution you are looking for. E.g. choosing in each iteration randomly two different numbers and switching them, while keeping the remaining in place would fit your description, but I'm guess this is not kind of thing you are looking for. I think you should clarify what do you mean by "correlated".