The present invention provides methods for determining the presence of immobilized nucleic acid employing unsymmetrical cyanine dyes that are derivatives of thiazole orange, a staining solution and select fluorogenic compounds that are characterized as being essentially non-genotoxic. The methods comprise immobilizing nucleic acid, single or double stranded DNA, RNA or a combination thereof, on a solid or semi solid support, contacting the immobilized nucleic acid with an unsymmetrical cyanine dye compound and then illuminating the immobilized nucleic acid with an appropriate wavelength whereby the presence of the nucleic acid is determined. The cyanine dye compounds are typically present in an aqueous staining solution comprising the dye compound and a tris acetate or tris borate buffer wherein the solution facilitates the contact of the dye compound and the immobilized nucleic acid.