Does a latin hypercube require uniqueness in rows? or only columns?

I was using the LHSdesign that matlab has provided to generate a latin hypercube design for a 32 run 6 variable experiment I am working on. I wanted to know the bin that each sample fell into so I used the following code to generate my run matrix:

%Generate a Latin Hypercube design of the proper size
X = lhsdesign(Np,Nv);
%Break the Latin Hypercube into its spaceing components
X = ceil(Np*X);

When I checked the output I noticed something that confused me, There were two different variables with the same bin number during the same run. Doesn't this violate the properties of a latin hypercube? or am I mistaken? please help. In the image below columns are variables and rows are runs.

Most papers I have found assume only uniqueness in columns, however the basic definition of a latin square is "an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. "