We expand the class of curves
(
φ
1
(
t
)
,
φ
2
(
t
)
)
,
t
∈
[
0
,
1
]
(\varphi _1(t),\varphi _2(t)),\ t\in [0,1]
for which the
ℓ
2
\ell ^2
decoupling conjecture holds for
2
≤
p
≤
6
2\leq p\leq 6
. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form
(
t
,
t
1
+
ν
)
(t,t^{1+\nu })
for
ν
∈
(
0
,
∞
)
\nu \in (0,\infty )
.