An imperfect DNA triplex, containing a pyrimidine/purine duplex with two sites of purine/pyrimidine base pair inversions, is formed and recognized. The unusual triplex is examined for the possibility of triplex DNA formation in a living system by way of non‐ideal sequence matching. The duplex part of it consists of a DNA oligomer with 17 nucleotidyl units, 5′‐TTCTTCTGATTCTCTCC‐3′ (C), which has two purine bases flanked by fifteen pyrimidine bases. The sequence of oligomer C is picked from a segment of cell cycle protein cdc25 gene (696 to 712) in Pneumocystis jirovecii, a yeast‐like parasitic fungus, which can cause pneumonia (PCP) in patients with impaired immunity. The complementary oligomer, 5′‐GGAGAGAATCAGAAGAA‐3′ (W), forms a DNA duplex WC with C, accompanied by CG/GC and TA/AT base pair inversions, in contrast to homo pyrimidine/purine duplexes. A third strand, 5′‐CCTCTCTTAGTCTTCTT‐3′ (H), combines with WC, to give an imperfect, but stable, triplex WCH+.UV absorption, circular dichroism, and native gel electrophoresis mobility shift assay are used to monitor the reactions at each stage. The triplex is stable in mild acidic solution, with a 1:1:1 stoichiometric ratio and a UV melting temperature (Tm) of 47.3 °C at pH 4.5. Isothermal titration calorimetry (ITC) and surface Plasmon resonance (SPR) unravel the thermodynamic information (ΔH = −123.1 kcal mol−1, ΔS = −378 cal mol−1K−1 and ΔG = −10.5 kcal mol−1) and kinetic rate constants (ka = 3.71 × 104 M−1 s−1 and kd = 7.49 × 10−4 s−1), respectively, for the WCH+ triplex formation process. WCH+ is termed an imperfect triplex since it contains two non‐canonical, non‐purine/purine/pyrimidine or non‐pyrimidine/purine/pyrimidine, base triads in the middle. This is the first time an imperfect but stable triplex, containing two purine bases in the middle of a pyrimidine‐rich strand (H), is formed and studied. The fact that an imperfect but stable DNA triplex can be formed gives great promise for drug design through more flexible targeting capabilities with much less stringent requirements, e.g., designs against Pneumocystis jirovecii using triplex formation in our example.