How to generate 256-bit random number within a range on embedded system

I need to generate cyptographically secure random number which is 256-bit long in specific range. I use microcontroller suited with random number generator (producer boasts that it's true random number, based on thermal noise). The upper limit of number to be generated is given as byte array. My question is: will it be secure, to get the random number byte by byte, and performing:

n[i] = rand[i] mod limit[i]

where n[i] is i'th byte of my number etc.