MATLAB - Best way of creating 2d array of unique pairs?

Question

What is the best way of creating a 10x2 matrix in matlab where each element is a random int between 1-5, and so that there are only unique pairs of elements in this array? I know randperm can give a me random unique numbers, but Im not sure if its possible to use randperm to give unique pairs? The only other way I can think of is using:

randi([1 5], 10, 2);

In a loop with an if statement checking whether all pairs are unique. An example of the data I would like would be something like:

4 5
1 3
2 2
1 4
3 3
5 1
5 5
2 1
3 1
4 3

Note: the order of the elements does not matter for example, both 4, 5 and 5, 4 would be valid.

Answer 1

First generate all possible pairs as rows of a matrix, then use randperm to generate a random subset of row indices:

N = 5;                                    %// alphabet size
M = 2;                                    %// number of columns
P = 10;                                   %// desired number of rows
allPairs = dec2base(0:N^M-1, N)-'0'+1;    %// generate all possible rows
ind = randperm(size(allPairs,1));         %// indices for random permutation of rows
ind = ind(1:P);                           %// pick P unique indices
result = allPairs(ind,:);                 %// use those indices to select rows

Example result:

result =
     3     2
     1     4
     3     5
     4     1
     1     3
     1     2
     2     4
     3     4
     5     5
     1     5

Answer 2

Here's another approach using randperm & dec2base without the memory overhead of generating all possible rows (quoting Luis's solution) -

%// Inputs
start = 1
stop = 5
Nr  = 10                    %// Number of rows needed
Nc = 2                      %// Number of cols needed

intv = stop - start + 1;                    %// Interval/range of numbers
rand_ID = randperm(power(intv,Nc)-1,Nr);    %// Unique IDs
out = dec2base(rand_ID,intv) - '0'+ start   %// 2D array of unique numbers

Sample runs -

Case #1 (Same parameters as listed in question) :

start =
     1
stop =
     5
Nr =
    10
Nc =
     2
out =
     1     3
     2     1
     5     3
     5     4
     5     5
     3     4
     2     3
     2     5
     3     3
     1     4

Case #2 (Different parameters) :

start =
        1025
stop =
        1033
Nr =
    10
Nc =
     5
out =
        1030        1029        1033        1028        1029
        1033        1029        1026        1025        1025
        1028        1026        1031        1028        1030
        1028        1031        1027        1028        1025
        1033        1032        1031        1029        1032
        1033        1029        1030        1027        1028
        1031        1025        1032        1027        1025
        1033        1033        1025        1028        1029
        1031        1033        1025        1033        1029
        1028        1025        1027        1028        1032