In this work, an ultra-low loss silicon nitride (SiN) edge coupler was designed and fabricated to interface with a single-mode fiber (SMF). Unlike other works that focus on the core structure, this work focuses on the cladding structure. First, it is demonstrated that the cladding structure ultimately determines the size and shape of the mode when the taper tip width is small enough. Then, the thickness of the up-cladding is optimized to provide enough space for mode expansion in the vertical direction. Air trenches are added to confine the mode laterally. In addition, the refractive index (RI) of the up-cladding layer is slightly increased to prevent light from leaking into the Si substrate. This edge coupler is then fabricated on the SiN platform at Chongqing United Microelectronics Center. For the TE mode at 1630 nm, a coupling loss of 0.67 dB/facet was obtained. At 1550 nm, 0.85 dB/facet and 1.09 dB/facet were measured for the TE and TM modes, respectively, which means that the polarization-dependent loss is 0.24 dB. Although the design method and the structure are based on a pure SiN platform, they are applicable to a silicon-on-insulator platform as well.