A method of ligating single-stranded nucleic acid comprising: a) combining in a reaction mixture: i) a hyper-thermostable lysine-mutant ssDNA/RNA ligase which is a mutated version of a precursor hyper-thermostable ssRNA ligase, wherein said precursor hyper-thermostable ssRNA ligase has a Motif I EKx(D/N/H)G (SEQ ID NO:32) and possess ssRNA ligase activity, but not ssDNA ligase activity, at a temperature of at least 75°C, ii) a first single stranded nucleic acid sequence with a 5' end base that is adenylated, and iii) a second single stranded nucleic acid sequence with a 3' end base; and b) incubating said reaction mixture at a temperature of at least 75°C such that said hyper-thermostable lysine-mutant ssDNA/RNA ligase ligates said 5' adenylated end of said first single stranded nucleic acid sequence to said 3' end of said second single stranded nucleic acid sequence to form a ligated nucleic acid sequence, characterized in that said hyper-thermostable lysine-mutant ssDNA/RNA ligase - has an amino acid substitution at said K (lysine) in said Motif I, wherein said amino acid substitution for said K (lysine) is an amino acid selected from the group consisting of: serine, cysteine, valine, threonine, and glycine, and - possesses both ssRNA ligase and ssDNA ligase activity at a temperature of at least 75°C. a) combining in a reaction mixture: i) a hyper-thermostable lysine-mutant ssDNA/RNA ligase which is a mutated version of a precursor hyper-thermostable ssRNA ligase, wherein said precursor hyper-thermostable ssRNA ligase has a Motif I EKx(D/N/H)G (SEQ ID NO:32) and possess ssRNA ligase activity, but not ssDNA ligase activity, at a temperature of at least 75°C, ii) a first single stranded nucleic acid sequence with a 5' end base that is adenylated, and iii) a second single stranded nucleic acid sequence with a 3' end base; and i) a hyper-thermostable lysine-mutant ssDNA/RNA ligase which is a mutated version of a precursor hyper-thermostable ssRNA ligase, wherein said precursor hyper-thermostable ssRNA ligase has a Motif I EKx(D/N/H)G (SEQ ID NO:32) and possess ssRNA ligase activity, but not ssDNA ligase activity, at a temperature of at least 75°C, ii) a first single stranded nucleic acid sequence with a 5' end base that is adenylated, and iii) a second single stranded nucleic acid sequence with a 3' end base; and b) incubating said reaction mixture at a temperature of at least 75°C such that said hyper-thermostable lysine-mutant ssDNA/RNA ligase ligates said 5' adenylated end of said first single stranded nucleic acid sequence to said 3' end of said second single stranded nucleic acid sequence to form a ligated nucleic acid sequence, characterized in that said hyper-thermostable lysine-mutant ssDNA/RNA ligase - has an amino acid substitution at said K (lysine) in said Motif I, wherein said amino acid substitution for said K (lysine) is an amino acid selected from the group consisting of: serine, cysteine, valine, threonine, and glycine, and - possesses both ssRNA ligase and ssDNA ligase activity at a temperature of at least 75°C. - has an amino acid substitution at said K (lysine) in said Motif I, wherein said amino acid substitution for said K (lysine) is an amino acid selected from the group consisting of: serine, cysteine, valine, threonine, and glycine, and - possesses both ssRNA ligase and ssDNA ligase activity at a temperature of at least 75°C.