Utilizing concepts of protein building blocks, we propose a de novo computational algorithm that is similar to combinatorial shuffling experiments. Our goal is to engineer new naturally occurring folds with low homology to existing proteins. A selected protein is first partitioned into its building blocks based on their compactness, degree of isolation from the rest of the structure, and hydrophobicity. Next, the protein building blocks are substituted by fragments taken from other proteins with overall low sequence identity, but with a similar hydrophobic/hydrophilic pattern and a high structural similarity. These criteria ensure that the designed protein has a similar fold, low sequence identity, and a good hydrophobic core compared with its native counterpart. Here, we have selected two proteins for engineering, protein G B1 domain and ubiquitin. The two engineered proteins share approximately 20% and approximately 25% amino acid sequence identities with their native counterparts, respectively. The stabilities of the engineered proteins are tested by explicit water molecular dynamics simulations. The algorithm implements a strategy of designing a protein using relatively stable fragments, with a high population time. Here, we have selected the fragments by searching for local minima along the polypeptide chain using the protein building block model. Such an approach provides a new method for engineering new proteins with similar folds and low homology.