Clique problem

Consider the clique problem: given a graph G and a positive integer k, determine

whether the graph contains a clique of size k, i.e., a complete subgraph

of k vertices. Design an exhaustive-search algorithm for this problem.

my answer

Step 1 S has to be assigned a k sized subset.

Step 2 Search for an edge in G for every pair of vertices of set S. If that fails go back to step 1 for another k sized subset.

Step 3 stop and return success.

is this right?