A right triangle with legs x and y and hypotenuse z in which x, y and z are all positive integers is called a Pythagorean triangle (PT) and the triple denoted by [x,y,z] is a Pythagorean triple. If x, y and z are all relatively prime (gcd is 1), then the triangle is called a primitive Pythagorean triangle (PPT) and the tripe a primitive Pythagorean triple. It is assumed that for any two positive integers m and n, with n [is less than] m, the three numbers x=2mn, y=m[squared] - n[squared], and z=m[squared] + n[squared] form a Pythagorean triple. It is the purpose of this short note to show how the PT can be constructed from the parameters m and n.