Secret sharing is a method of distributing a secret among a group of participants such that if (i) an authorized set of participants cooperate, then they can reconstruct the secret and (ii) an unauthorized set of participants can’t recover the secret and doesn’t know anything about the secret. In 1994, Joan Cooper proposed a secret sharing scheme based on the critical set of Latin square[3]. This has some drawbacks. In 2015, Rebecca J. Stones published a secret sharing scheme based on autotopism of Latin square[1]. The scheme solves all the issues associated with the Cooper’s scheme. However, we noticed that, her scheme has the following shortcomings: (i) The scheme construction is limited to a particular pattern of the Latin square only, (ii) The scheme works only as k-out-of-k technique and not as a proper threshold scheme, and (iii) the dealer is the central part of the whole process, if he is dishonest then the whole secret is revealed. So, in this paper, we modify Rebecca’s scheme so that it works (i) for a couple of more contours with only one autotopism, and (ii) as a t-groups-out-of-k scheme. So to reconstruct the secret anyone of the available t groups can cooperate and recover it. That is, the modified scheme could reduce the key availability problem to some extent. As a byproduct of our modification the security from the brute force attack increases as well.