A method for detecting a target nucleic acid sequence from a DNA or a mixture of nucleic acids on a solid phase using a dual-labeled probe with resistance to a primer-independent 5' to 3' exonuclease activity of a DNA polymerase, comprising: (a) hybridizing the target nucleic acid sequence with an immobilized probe having a nucleotide sequence complementary to the target nucleic acid sequence; wherein the probe immobilized on a solid substrate through its 3'-end has an interactive dual label comprising a reporter molecule and a quencher molecule; the interactive dual label is positioned on the immobilized probe to induce energy quenching between the reporter molecule and the quencher molecule; a first label and a second label are selected from the reporter molecule and the quencher molecule; the first label is linked to the 5'-end of the immobilized probe and the second label is linked to a base of an internal nucleotide placed downstream of the first label, such that the linkage of the second label permits the internal nucleotide to have resistance to the primer-independent 5' to 3' exonuclease activity of the DNA polymerase; (b) contacting the resultant of step (a) to the DNA polymerase having the primer-independent 5' to 3' exonuclease activity under conditions for cleavage of the immobilized probe; wherein the immobilized probe hybridized with the target nucleic acid sequence is digested by a primer-independent exonucleolytic reaction of the DNA polymerase to release the first label from the immobilized probe, resulting in change in a signal on the solid substrate; (c) terminating the exonucleolytic reaction of the DNA polymerase at the internal nucleotide labeled with the second label; wherein the termination of the exonucleolytic reaction is induced by resistance of the internal nucleotide having the base linked with the second label; wherein the linking of the second label with the base confers the resistance to the primer-independent 5' to 3' exonuclease activity of the DNA polymerase to the internal nucleotide having the base linked with the second label; wherein the second label is remained on the solid substrate; and (d) detecting the signal change on the solid substrate, such that the signal change by the cleavage of the immobilized probe is indicative of the presence of the target nucleic acid sequence. (a) hybridizing the target nucleic acid sequence with an immobilized probe having a nucleotide sequence complementary to the target nucleic acid sequence; wherein the probe immobilized on a solid substrate through its 3'-end has an interactive dual label comprising a reporter molecule and a quencher molecule; the interactive dual label is positioned on the immobilized probe to induce energy quenching between the reporter molecule and the quencher molecule; a first label and a second label are selected from the reporter molecule and the quencher molecule; the first label is linked to the 5'-end of the immobilized probe and the second label is linked to a base of an internal nucleotide placed downstream of the first label, such that the linkage of the second label permits the internal nucleotide to have resistance to the primer-independent 5' to 3' exonuclease activity of the DNA polymerase; (b) contacting the resultant of step (a) to the DNA polymerase having the primer-independent 5' to 3' exonuclease activity under conditions for cleavage of the immobilized probe; wherein the immobilized probe hybridized with the target nucleic acid sequence is digested by a primer-independent exonucleolytic reaction of the DNA polymerase to release the first label from the immobilized probe, resulting in change in a signal on the solid substrate; (c) terminating the exonucleolytic reaction of the DNA polymerase at the internal nucleotide labeled with the second label; wherein the termination of the exonucleolytic reaction is induced by resistance of the internal nucleotide having the base linked with the second label; wherein the linking of the second label with the base confers the resistance to the primer-independent 5' to 3' exonuclease activity of the DNA polymerase to the internal nucleotide having the base linked with the second label; wherein the second label is remained on the solid substrate; and (d) detecting the signal change on the solid substrate, such that the signal change by the cleavage of the immobilized probe is indicative of the presence of the target nucleic acid sequence.